Oops, I'm so sorry that I hadn't thought about your reply.
Then I'll tell you the questions you said.
First, the word '제' is not only a compound word with '저' and '의,' but just a different way to say '저.' I think you have a tendency that a word from English must be altered to only one Korean word, but it is not true for them and every couples of language as well. In Korean, 'I' can be translated for '저가,' '제가,' '저는,' '나는(the normal form),' '내가(it is, too),' etc.
Your second asking is also equal to the first.
Thank you for replying. ;)