What are the rules regarding land ownership for a pruzbul?
Yad Avraham in Uktzin 3:10 quotes a gemara in Bava Basra stating that for a pruzbul to be effective the debtor (one who owes money) must be a landowner.
Would a car make someone a landowner in this context?
The gemara in Gittin 37a answers your question (translation R Steinsaltz) that one needs a very small amount of land and it can even be lent to the debtor.
We learned in a mishna there (Shevi’it 10:6): One may write a prosbol only on the basis of the debtor owning land. If the debtor has no land, then the creditor transfers any amount of his own field to him so that he can write a prosbol. The Gemara asks: And how much is sufficient to be classified as any amount? Rav Ḥiyya bar Ashi says that Rav says: Even the amount of land sufficient to grow a stalk of cabbage is sufficient. Rav Yehuda says: Even if he lent him a place sufficient for an oven and a stove, one may write a prosbol on this basis.
This is codified by the Rambam MT Shviit 9:19
Since a car is not land, it cannot serve as a basis for a prozbul. But one who doesn't own land is commonly lent the amount required (see e.g., instructions from the OU, p. 2, point 5).
Note also the a prozbul is only written at the end of the seventh year, since debits acquired it is written are not prescribed (MT 9:22).