1) Does it always have the meaning of increasing, growing, building up? What is the opposite?
As a verb, 수록하다 has meanings of "to contain" or "to record", it is different from the connecting ending, -ㄹ수록.
-ㄹ수록 can mean, "the more.. the more(빠를수록 더 좋다: The sooner, the better)"and "the less.. the less(말하지 않을수록 좋다: The less said about it, the better)"
2) Can it be used in past and present forms as well as future (like any other modifier + noun)? 한 수록 = the more you did; 하는 수록 = the more you do; 할 수록 = the more you (will) do
This connecting ending takes the form -ㄹ수록 always, there's no these form, -ㄴ수록 or -는수록.
3) Can it be used with adjectives? Or maybe only with the "to become adjective" form? 예쁠 수록 = "the more pretty you get". 예뻐질 수록 = as you become prettier
-ㄴ수록 can take both verbs, adjectives
Hope it'd help you. ^^