Civilization – Can’t purchase Great Prophet

I can't answer the first two questions in a definitive manner. However the rest I can handle:

How would the game work (i saw somewhere else it's RTS style)?

It's not quite RTS, but it's not turn-based either: every human player takes their turn at the same time. Once all players click "next turn", the AI civilizations, city states and barbarians all take their turns in order. Then the human players' next turn begins.

This causes some big issues when interacting with other players, and is a big griping point for many. For example, wars became a battle of who can click first - if I can blow up your unit before they get a chance to attack, then I'm in a hugely advantage position. It's unfortunate to the point where a lot of us don't even both with multiplayer (except cooperatively with friends) because when everyone moves at the same time, the game loses a lot of the carefully planned strategy you get in single player.

It's worth noting that once you click "next turn", you can't do anything even if other players are still moving - so it's to your advantage to delay the end of your turn a bit in case something comes up.

How long will the game take to complete?

Depends highly on the number of players and the game speed, but significantly longer than a single player game of the same settings. Some turns you may be blazing through waiting for construction while another person is taking his sweet time waging war, and vice versa. Even playing on quick/small map can take hours. Set aside a large chunk of time.

Can I take a bathroom break without abandoning my civ temporarily?

Yes, you can just sit on the "next turn" button and not click it while you do something else. You would just hold up everyone else from getting to the next turn.

Can I chat to the other players?

Yes. There is a chat box that appears in the top right corner of the screen.

In general I agree - in late-game, GP are less useful and I usually trade them in immediately for a quick golden age. However, unless you have absolutely everything, great scientists and great engineers do have some value, and there are use-cases where the rest are useful as well, I've listed them below.

Remember golden ages are always great, even if they are short. +gold, +production and no happiness issues.

Great Scientist: if you already have everything then this is indeed useless, but as long as you don't this is still useful. It's true late-game technologies are usually researched quickly but there are a few wonders in late game and being the first to reach them can be nice; furthermore, being the first to unlock Aluminum or Uranium is good because you can plan your land acquisitions better.

Great Engineer: there are some wonders in the late game, and they are pretty good actually. Other than that, great engineers are useful if you create a new city in the late-game; I usually buy a lot of buildings whenever I do this, but a great engineer can save a lot of money by speeding the most expensive buildings.

Additionally, factories are always useful.

Great Merchant: whether you should use the diplomatic mission or the golden age is not always obvious - see my answer to another question to see my opinion. In general I say a diplomatic mission is usually worth more gold, but a golden age also nets production. Custom houses are not worth it, in my opinion.

Great General: I almost always trade them for a golden age immediately, with one exception - I sometimes build citadels in natural chokes or other appropriate locations. From experience, a single citadel in the right spot, backed by 2-4 units, can stop an army.

Great Artist: the most useful type in the late game! Using the culture bombs allows you to reach practically everywhere. I one time used 3 of them to get to just one Aluminum patch in the middle of an icy area (just took a little time because of the cooldown). They can also be used to steal stuff from civilizations and city-states.

Also, landmarks are always nice in cities that already have a lot of +% culture.

Regarding city states: I usually do use great people from city-states, late-game maintenance costs are high but I think a golden age is always worth more than the time it takes them to get to the nearest border, even if it's a golden age lasting just 3 turns.

EDIT as of the June 2011 patch, great person improvements have been buffed:

• Erecting a great person improvement automatically connects a strategic resource if there's one on the tile
• Each great person improvement has an associated technology which increases the tile yield when researched
• Completing the freedom tree doubles the tile yield

This means using great people for improvements is a more viable option now.