I can vouch for my answer from the perspective of how philosophers in general (and philosophers of language at the introductory level) answers this. For linguistics, I include what I was able to glean, but apparently there's a large diversity of opinion on these questions.
1 A: I have a car
2 B: Sorry?
3 A: I have a car
4 B: You have a car
5 A: Yes.
First, off I've taken the liberty of changing 1 and 2 to A and B, so that we can put line numbers on the front.
Now to give some simple definitions and see where things lie:
If we take utterance to mean
a distinct instance of verbal linguistic expression often seen as interrupted by silence.
Here, in the conversation you post A makes 3 utterances and B makes 2 utterances. So there are 5 utterances since utterances always carry with them the specificity of when they are uttered. Apparently, there's disagreement about what constitutes an utterance.
Wikipedia claims that a sentence in linguistics is
a textual unit consisting of one or more words that are grammatically linked.
On this type of definition, I would actually count 5 sentences -- one for each utterance because no utterance here contains multiple sentences, and the units are broken by the utterances (sentences) of the other speaker. I would count 4 distinct sentences because "I have a car" is repeated.
In philosophy, proposition, it is a claim about the world that can be either true or false. On this definition, there is only 1 clear proposition that occurs throughout:
A has a car.
Lines 1,3, and 4 are expressions in sentences and utterances of this same content. Yes, the "I"/"you" varies but it doesn't change the content of the proposition.
Line 2 would not be a proposition in philosophy since a question is not true or false.
It might be possible to argue that the final line (5) A: "Yes" contains a second proposition or repeats the first one.
A affirms/confirms that the proposition A has a car is true.
But unless there's some special reason to be so pedantic, I wouldn't draw out a second proposition from it.
In the definition of proposition used by SIL's linguistics glossary,
A proposition is that part of the meaning of a clause or sentence that is constant, despite changes in such things as the voice or illocutionary force of the clause.
If I'm reading it correctly there are two or maybe even three propositions here,
1,3,4 = A has a car.
2 = B is sorry [presumably for misunderstanding A or something like that?]
5 = either same 1,3,4 or the same issue as identified in the philosophy account (is it a repetition or a claim with respect to the claim).
Apparently these terms are used in very different ways by linguists in different subdisciplines.