I was given the Magos Biologis Secrets skilltree, but the Heroic Deed for it is not finished yet:
I have only a crusader as my character (so, no other char that could unlock skilltrees for my crusader), and that skilltree did not show something about level as a requirement (like the movement skilltree does).
And it did not belong to my starting skills as a heavy weapon crusader, those were ranged attacks, area attacks, and defense (at least I did not have it at the start...).
Yep, each class has a own set of skill trees if you start to play. E.g. assasin has the Movement skill tree, crusader doesn't. If you unlock a skill tree this means all your classes have now access to it (so unlocking the movement skill tree with a crusader you wont see a change on your assasin, but you will have it on your cursader and psyker also)
Some of the trees unlock with your level I believe, based on your class.