Panopticon covers many general ideas of basic habitat living infrastructure and the like, though that's slightly more geared toward space than planetary living. Others have hit most of your points, but I'll give my understanding.

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Food:

Welcome to the beauty of public nanofab. So long as Makers have a steady flow of power, they can recycle organic matter and water and can produce basic "food". Of course, in the Planetary Consortium the level of quality for public and even consumer-level private fab tends to be low unless you're very rich. So as discussed in some earlier threads, people probably hit up the corner shop or the farmer's market. Some of the food you buy is synthesized (vat-grown cloned meat, synthesized drink powders, premixed maker paste which prints any kind of noodle you like), others are grown fully. Mars does this in agridomes mentioned a couple of times in the text, outside the major cities. Huge open sprawling ranches or farms are beyond Mars as written, but contained and controlled domes can grow staple crops and handle low-impact livestock like sheep, goats and alpacas. Luna has large volumes of green space in their caverns (as do many Cylinder habs) which can serve similar purposes. What and how they grow it is up in the air. It probably involves lots of drones, and may be assisted by nanoswarms or smart animals. AI oversight is probably common, though obviously you need humans to manage and maintain operations. Like everything, some are probably wholly-owned or run by microcorp scale enterprises, but there is a food-related Hypercorp, Prosperity Group IIRC, and they hold a [i]big[/i] share in the Hypercorp Council. How does it get to you in the city, you ask? Well, the beauty of Eos rail! Mars has less surface area than Earth and only a handful of major city destinations. Any major farming community probably hooks up to the maglev lines at some point and ships it in. Huge supermarkets and sprawling malls are probably done for - too space inefficient, but any given neighborhood probably has a decently sized grocery outlet - probably brand name. If you have cash, I'm sure you can arrange delivery either direct from the store or with another service, like Amazon is doing now. Otherwise, most households are said to have access to at least one Servitor bot. Restaurants, yes. Food stands, also probably yes. Go into a small neighborhood, or hit up the souks outside the dome, you'd probably find a lot of little industry like that. Remember, with the right licenses (or the right hacks) you can put your entire means of production in your back room.

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Water:

Well, the Panopticon quote covers core infrastructure and recycling in a hab space itself. This applies to basically everywhere which isn't Mars or an oceanic moon. There are a couple of things to remember about Mars in this regard. First is that Mars is undergoing terraforming - basically growing a biosphere. Just pumping the water straight to you is a waste, that water needs to build a natural cycle. Melting the ice caps, permafrost fields and dropping iceteroids is all about building water levels on Mars. One of the books describes a terraforming worker (which would mostly be done by the Martian nomads) finding an ice field and planting thermal rods in it to melt the ice and make it liquid. The second is that basically every major city on Mars is or will be waterfront property. Artificially made rivers actually flow through them. So while Mars isn't up to rain storms or wetlands or any of that, there is a steady enough flow of water for that. From there it's just recycling infrastructure. Smaller habs probably have to ship in ice from the poles to keep their recycling levels up.

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Hospitals:

Again, Panopticon handles the general infrastructure of all this. So under normal circumstances, you're dealing with Poison Control and Accidents. Now, Medical Care is a service, and in placed like the Planetary Consortium, that means you have to pay for it. If you have a job - this is no problem. If you do not have a steady source of income, well, you better be able to pay those emergency room fees otherwise it's another indenture stint for you. What kind of health care plan you have probably decides how you get your care. Some services might send a couple of paramedics (or just a Dr. Bot) over to your house and treat you there, or haul you to your local trauma center (I'd assume every dome has at least one) for more serious treatment. Anything that can be handled with drugs is like how you handle groceries. If you have Mesh inserts, you have biomedical sensors you or your muse can cross-reference, then order out to the "drug store" and get whatever you need made right away in a specialized medical Maker. Doctors and Nurses probably exist. Nursing jobs probably used to be handled by AI in Ayah pods, but there's a lot of desire for additional security in that regard. You might see more indentures doing that kind of job if any of them had basic medical experience. Doctors, also yes, because nanomedicine can be regulated, and not all problems are solved by just rubbing some nanos on it. You'd need a medical professional to figure out what treatment you need and to push the buttons on the vat. Plus, if you been in an accident (or a gunfight) you might need a personal touch to pull those dimondium hyperglass shards (or depleted uranium flechettes) out of your chest cavity before you go in the tube. At the very least, a robo-doc with hands.

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Security:

Well, yes, most banks are electronic. I don't think there's a solid "cash" equivalent to an Inner System Credit, and even if there is it's probably a portable electronic storage medium. "This chip contains 2,000 credits", or something. If you want to be covert, you barter or deal in Crypto-Cred. Now, on Luna, they have a strong banking history. Due to their age and prestige, it is quite likely Lunar banks have big buildings, physical lobbies and have vaults and safety deposit boxes to hold your very valuable physical things. Mars, probably less so. Most of Mars is recent immigrants, lots of them ex-indenture. They're not likely to have high physical security needs. But there may be a few branch banks which have deposit boxes so you can store valuables not in your capsule apartment. The security measures are going to be future materials doors, the best data sec money can buy, and round the clock infomorph monitoring. If they don't employ private security, you know there's a red phone to the local PD tactical unit. Hypercorp security is the same, only with more money to throw at the problem. Hypercorps definitely have some physical locations - if nothing more than server rooms to host "virtual offices" or research park holdings to do R&D in. If you want to know what police response is like, you'll need to check per habitat. Mars, for instance, has a section on each city's law enforcement in [i]Sunward[/i]. In general, any space people are in which is not ultra-secure has either direct police access to internal sensors, or access with a warrant. Beat cops exist, probably mostly in flying cars and with just-short of riot gear. Panopticon even says cops on duty in Valles-New Shanghai double as public surveillance feeds. But when the big guns get pulled, it's tactical response. Which is basically paramilitary level - seeing as there is no codified martian military branch. Exoskeleton riot cops drop from VTOLs and say "your move, creep". So depending on what kind of threat level a group presents them as, they bring as much noise as they think they need.

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Living Cost:

Okay, here, you need to do a little digging. In [i]Transhuman[/i], there is a system for handling living expenses/lifestyle cost on a monthly basis - using the same cost levels as gear. It gives a description for what kind of lifestyle you can expect at that cost level also. It's very abstracty, but a good way to put things in mechanical terms. 500 is either in the upper [Low] range or the lower [Moderate] range, so that PC may have just offered to pay a decent chunk of a beat cop's monthly expenses. Keep in mind that's just bills, food budget, maintenance, etc. For other costs, you kind of have to infer from this system. The game kind of lumps everything together. Now, for the trailer of your question - that's dependent on your hab. The LLA is highly paranoid about projectile weapons like guns (Though in a recent topic, it came up that this is overblown - it's an inconvenience which has been inflated to a public menace), while Mars is likely more loose. But in general, if you can buy personal protection, you can probably have it in some form. Prostitution is definitely legal, there's lots of discussion about "adult entertainment" as an indenture contract (and a short and lucrative one at that). How this is organized is probably up to you. Street-walking probably isn't as common (and might violate your local business regulations), but clubs, dollhouses and other establishments wouldn't be too hard to find. Drugs is probably a similar prospect. You get your product from a legit source, you can sell most anything - most drugs aren't nearly as harmful or limited as many modern substances (though probably a few of those running around). Regulations would be on the serious performance enhancers and combat drugs than anything recreational.

Two things to add to the comments above; For medical you asked about why have medical if everyone has healing vats. First off, not everyone has healing vats. They are very expensive. Also, I don't believe they are intended to be fully automated. They heal up damage via nanite magic but bones still need to be set and wounds still need to be closed or else the nanites might heal them up wrong. IRL you go to a hospital for a lot of reasons beyond 'they make it heal faster'. The vat will make things heal faster but it can't provide any (or many) of those first services. As for banks, one thing I could definitely see banks still being needed for is feedstock. Rather than physically retaining possession of feedstock that isn't immediately going to be reused you could take the material to a bank where it is logged and placed in the bank's reserves. When you need that material at a later date you withdraw it and are issued the correct amount from the bank's reserves. Naturally there are also a variety of services such as feedstock exchanges which can be handled through the bank (I need 2 kg of lead to make some bullets so I trade in 1.2 kg of iron that I have in my account).