me and my wife's

What do Americans say when they have to form a possessive where there's at least one pronoun?

- That's our car, me and my wife's. /...my wife's and mine. /...etc.
- Me and my friend's project is about... / My friend's and my project... / My firend's project and mine... / etc.
- My first name and my uncle's are the same. / My uncle's and my first name... / etc.
- That's their car, that's his and hers.
- That car is Tony's and hers. / ...is her and Tony's. / ...etc.

Could somebody help me and give me some examples? I have no idea, and I've only got prescriptive advice so far. I'm interested in what Americans are likely to say (and sounds good), not weird rules. Thanks.

I'm an American native English speaker

- That's our car, me and my wife's. /...my wife's and mine. /...etc.
*That's our car, me/mine and my wife's
OR
my wife and I's (clitic expression) [not correct, but it's what you'll hear]

- Me and my friend's project is about... / My friend's and my project... / My firend's project and mine... / etc.
*Me/Mine and my friend's (where me/mine is used, "me' is heard more often) project

- My first name and my uncle's are the same. / My uncle's and my first name... / etc.
*Me/Mine and my uncle's names are the same

- That's their car, that's his and hers.
*That's their car, that's theirs/his and hers

- That car is Tony's and hers. / ...is her and Tony's. / ...etc.
*That car is her and Tony's

The main case where there really is a relatively fixed order, at least in everyday spoken North American English, is when there is a pronoun being used in a coordinate construction with something that is possessed with the equivalent possessive determiner. In that case, the normal word order used in everyday speech is to place the pronoun first (such as "me") and then after the conjuction place the second item with its possessive determiner (such as "my"). While due to prescriptive influence you may hear things like "my wife and I's", the more natural word order is "me and my wife's".

One important note is that in everyday speech, it is normal to actually use oblique case rather than nominative case for pronouns in such coordinate constructions as subjects; in particular, you will never hear "I and my wife's" but rather only the normal "me and my wife's" or the prescriptive "My wife and I". Note that this restriction is not as strong for pronouns other than "I"/"me", but it is still normal to say things "her and her brother" or "him and his car".

Thank you so much. I still have some doubts though.

<<Me/Mine and my uncle's names are the same>>
I was told that when something is not in common, I should add the possessive S to all of the owners. --> Tom has a car. Bob has a car. --> Those are Tom's and Bob's cars.
So I don't understand that example. Me and my uncle's names? Like, if I had a car and Bob had another one, would you say "Those are me and Bob's cars"? Seems weird, unless we both own both of them, which is not the intended meaning.

Also, I was thinking that there might be some problems sometimes. If I say "Me and my wife's friend went downtown", it would be taken as "My wife's friend and I went downtown", wouldn't it? So I guess if I wanted it to have the other meaning, I should say "Our friend, me and my wife's friend, went downtown". Right?

<<One important note is that in everyday speech, it is normal to actually use oblique case rather than nominative case for pronouns in such coordinate constructions as subjects>>
Yep. With first person singular pronouns it seems to be like either "Bob and I are..." or "Me and Bob are...", but in the other cases it almost seems to work the other way around (so it's "He and Bob are..." instead of "Bob and he are...", and "Bob and him are..." seems more common than "Him and Bob are...")
But of course this is just my opinion and I'm not sure. I learned about this by surfing the net and googling around.
Thanks again.

<<Tom has a car. Bob has a car. --> Those are Tom's and Bob's cars.
>>

For this you would say: Those cars are both Tom's and Bob's. ('Both' refers to Tom and Bob, not the number of cars. As in the "Me and my wife's friend went downtown" example, *stress* would indicate which you meant it to be.)

But if you put Bob's car and Tom's car together, those are "Bob's and Tom's car", right? And not "Bob and Tom's cars". So I was wondering what I should say in cases like:

Delete my name and my wife's first name --> Delete my wife's and my first name? My wife's first name and mine? Not "me and my wife's first names", because they are two separate names, I think.

So I suspect that possessive constructions with pronouns are only used when all the owners share the same thing (= "that's me and my wife's house"), but not when the things are owned by separate people. I think I have to say either something like "That's Bob's car and my car" or "That's Bob's car and mine" (two cars).

I am now realizing that this is actually pretty complicated, since context and intonation are likely to change the meaning considerably.
Anyway, I'll appreciate your opinions. Thanks.