>>213582203
Yes, all of them are correct. Those three usually mean the same thing,
>(a)"He always studies at the library,"
but there is still some ambiguity.

Sentences 1 and 2 could also mean
>(b)"The place where he studies is always the library."
Sentence 3 could also mean
>(c)"He does not do anything other than studying at the library."
To remove the ambiguity, you can say
>彼が勉強するのはいつも図書館だ。
for (b) and
>彼は図書館では勉強だけをする or 彼が図書館でするのは勉強だけだ。
for (c).