Although bwarner's answer was helpful as always, no one verified beyond "I think so" that puppet cities are affected by each of the civilization wide effects, so I did some testing and:
Yes, puppet cities are affected normally by all civilization-wide effects.
I can't verify that there are no exceptions, but I verified at least one of each of the things I was concerned about...
The Testing
Civilization Special Trait
I loaded up France on easy, and went about conquering. Japan fell, giving me Kyoto to play with. As soon as I conquered the city and took it as a puppet, it was producing 2 culture. This matches perfectly with France's ability, so CHECK!
More Test Setup
Having acquired my victim, I setup the test: social policy ready, golden-age ready, and wonder ready all on the same turn! (Save file available upon request, whenever I get around to it after that.)
Before
Social Policy
I enacted Liberty->Republic, which gives +1 production/city. That matches, so CHECK!
Golden Age
I already had culture working for me, so I started the golden age by enacting the social policy Piety->Reformation. Clearly shows an increase in both gold and production, CHECK!
World Wonder
If you take a look at all of my cities from the same turn, you can see Orleans is about to finish the Sistine Chapel, which gives +33% culture/city. I went to the next turn, and without any growth or buildings completing, the after shows increased culture on Kyoto. (Lyon also started with 7 culture and ended with 9 as well, so the rounding definitely matches.) CHECK!
Everything checks out. I suppose puppets really are just normal cities that you don't control. I would still love to hear if anyone finds any exceptions!
No, a tile may only be worked by a single city on any given turn.
If you tell a city to work a specific tile that another city is already using then the other city will be forced to stop working it. It is possible to get the other city to start working the tile again (but only by stopping the new city from doing so) - the tile is never "locked" to a particular city.
You should determine what bonus output the wonder has and then try to work it from a city that takes the most advantage of that - so if you have a gold-generating wonder, let a gold-generating city work the tile, for example.
Best Answer
There's a GameFaqs thread discussing this, here is a list one of the users there compiled:
When any player on the team researches the tech tree all of the teammates get the technology. If you both research the same tech at the same time, the time for completing it will be halved.
You also see the map under fog of war which is cleared by the other player on the team.
If any player on the team declares war on someone, the whole team goes into the war.
Also, the the points of everyone in the team will be counted together and it shows a team score at the list on the right.
You can gift units (both combat & civilian) to your teammates just like you can for city-states normally.
However you won't automatically share luxory- & strategic resources, but the standard trading mechanics work as normal so you can trade half of what you have over to your teammate for example.
You have permanent Declaration of Friendship with each other
You'll still feel ideological pressure (reduced happiness for adopting different ideologies) from team mates
Autocracy tenet Futurism doesn't work against team mates.
As he mentions himself, there is probably more.