It is a bit ambigous, you are right. But the rule is, if there is more than one subject in a sentence, you wouldn't omit them. So for example it is wrong to say "yersin ve içerim" for "you drink and I eat". Similarly here if you were talking about a 3rd person, you would say "O ödevi bitirince (sen) beni ara".
From what I understand, "bitmek" is when the subject itself finishes, where as "bitirmek" is when the subject finishes something other than itself. For example, "ben bitirdim" (I finished [something]) vs "ben bittim" (I am finished, as in I am exhausted, my life is over, my fate is sealed, etc).
Someone please correct me if I am wrong. :)
Exactly the same as the dictionary :)
I found this on a different issue. Not what you're looking for, but provides something different.
Eğer zorluk çekersen bana gel. (Come to me if you have difficulties.)
Can a native english speaker help me out here? (I know we're learning Turkish here but I got the sentence wrong because of English...) Why is the "the" necessary here? I keep getting this wrong but I feel like it sounds better to say "Call me when you finish (your) homework"
"Call me when you finish the homework" means that there is a specific piece of assigned homework that the speaker and the hearer both know is being referred to. "Call me when you finish your homework" merely means that the hearer has unspecified tasks assigned by the teacher, but not any specific piece of work. "when you finish" means call at once when the homework ends; the calling and the ending are synchronous. "when you have finished" merely means call sometime after the homework session ends; probably fairly soon after, but not synchronous. However, native speakers are pretty lax about the difference, and might use any of these versions, meaning pretty much the same thing: "Do your homework, then call me". Hope that helps:)