Technically speaking, I don't feel there is the difference between them. Both are the same as for me, but I think "~하기위해" is more often used. In conversations, we prefer to use "~하려고" instead of them. Here is thing how I feel about "~하기위해서" 1) "~하기위해서" is kinda emphasis of "~하기위해" so you can put a stress on "서" as in "위해서". 2) When I read a sentence with "~하기위해서", I take a breath after this phrasal. For example, 나는 대학을 가기위해서(pause - take one breath)열심히 공부했다. 3) Sometimes we can make a sentence putting "는" as in "하기위해서", but not for "하기위해". For example, To speak Korean well, it's a good idea to watch Korean dramas on TV. (한국어을 잘 말 + 하기위해서 + 는, 한국 드라마를 보는것이 좋다) 4) "~하기위해서" sounds more appropriate in written rather than "하기위해" It's just my two cents.:)

You can ommit 서 or use 서 either way is OK in this case of ‘in order to’ ~ 하기위해서

"WHEN DO I USE" is "언제써" in Korean.

I read that Form action when I read it first.

Formation < no space