Learn Russian: Мы спорим насчёт последней правки.

While о (plus prepositional) and про (plus accusative) are the standard ways to say "about," насчёт is more specific and translates better to "regarding" or "concerning." It is slightly more formal and focuses the argument on a specific issue or matter.

Why do последней and правки end in -ей and -и?

The preposition насчёт always requires the genitive case. Since правка (edit) is a feminine noun, it changes to правки in the genitive, and the feminine adjective последняя (last) changes to последней.

Is правка the most natural word for "edit" here?

Yes, правка refers specifically to a correction, revision, or edit made to a text, document, or code. It comes from the verb править (to correct or edit). If you meant a general change in plans or circumstances, you would use изменение instead.

What would it mean if we used the perfective verb поспорим instead of спорим?

Мы спорим is imperfective, describing the ongoing process of "we are arguing." If you used the perfective поспорим, it would change the meaning to the future tense: "We will have an argument" or, very commonly in Russian, "We will make a bet."