"~たい"-form and associated particle usage

My question is about the "~たい"-form ("want to").
I know that in a sentence containing this form, you can use は to mark the person who desires something. For example, "私は、東京に行きたい".

But then I came across this sentence:

あなたが一番したいことはなんですか？

I translated it as "What is the thing you want to do most?". So here, が is the particle used to mark the one who desires something.

Now, for my question: Can が always be used to mark the one who desires something in a "~たい"-sentence, or is it something that is limited to relative clauses such as the one in the second example?

In extension, is it okay to say "私がケーキを食べたい" or "私がケーキが食べたい"? Sounds a bit strange to me, but then again, my Japanese isn't really great yet.
But anyways, thanks for reading through my question!