There's Tick functions in Actor and Window classes. Can I make similar or use something instead in other custom class (derived directly from Object)?

Yes, but you'll have to call it yourself.

Hmm thats very interesting, Tick function is firstly declared in Thinker class. Aren't there any restrictions of making custom class Thinker's child? Maybe I simply derive it from Thinker. What time units deltaTime uses?

The only limitation of a thinker is that it must belong to a level. It uses seconds.

And how may I make it belong to Level? I know only that thinker is created using NewSpecialThinker().

I think that once you create the thinker in the current map it belongs to it, but I could be wrong.