Hi, I hope I can clear some of this up for you.
1. Is 'Looks' the same as 'Seems'?
You can say 'it looks like delicious', only if you are directly looking at it. You can say 'it seems delicious', is someone is describing something to you.
So if you can directly see the thing you are describing, then say 'it looks like', but if you simply know what it is, or someone is telling you about it, then say 'it seems like'.
Lastly, if you've seen someone play a game of soccer before, and a friend asks you to play, you can say, 'I have seen people playing soccer before, it looked like fun' (past tense).
2. 'Studying' and 'by studying'
Simple. I want to become a doctor by studying at college. I am studying medicine. In this case, before the verb, the 'by' indicates a mode of achieving the first statement (I want to be a doctor). Exactly the same as you would say, 'I want to get to school by walking'.
3. 'Find someone with whom to go out' and 'find someone to go out with'
I can't really see a difference, however most English-speaker rarely use the word 'whom', even when it's grammatically correct. Especially in speaking and writing with friends, I would chose 'someone to go out with'.