"Top layer" plywood subfloor fastened to decking
The 45 degree decking is the primary sub-floor.  It's a technique that was widely used in the past, but has subsequently been replaced with simply dropping sheets of plywood down.

In answer to your questions:

1) You can glue and screw to the sub-floor.

2) In this case, it doesn't matter.  The sub-floor is carrying the load diagonally.  However, if there were no sub-floor, then you would want to go perpendicular. See this discussion on the subject.

3) Always - always - always level as you go.  Fix the level at the soonest possible opportunity or it can be amplified by an order of magnitude.