A first cause is logically necessary
Your goal is to argue from a basic premise to a conclusion where "1." randomly states what should be the penultimate point but then discards it.
If you instead argue, for any object that exists (however defined), it has a prior cause or it does not (and if it does not then it is a foundation - can be a proposition with justifications if this is hinged on too much for people).
Then you can insert any trivial object x through that (it must be trivial otherwise you need a new proposition just so long as they accept it).
I suspect a large amount of the work done is justifying "prior cause". Whichever argument justifies that (from a basic premise) should be prior.
In any case, because your work is written that way, you cover a lot of ground twice and inefficiently work with what you've been given. You can really write that all in one line (∃x(Px OR !Px & Fx) - there exists x such that it has a prior cause and if not then it is the first cause).
Edit: Notice x or !x is trivially true and valid no matter what proposition for classical logic but the & adds something so a separate proposition is necessary where you could write Px > !Fx, ∃x(Px OR !Px) as two lines.