...let's suppose If I occupy one hex during the normal Movement Phase and that a blitz phase is launched by me by another HQ after the normal movement phase. May I then exit from a battle adyacent to this new friendly hex as a phase has finished and therefore I have consolidated the ownership of the Hex (the one where I moved in the first movement phase (the one before the blitz)?.
If I understand your question correctly, the answer is yes. If a hex becomes friendly during the first phase of a turn, then units can disengage into that hex during the blitz phase. You will see this a lot in the first German turn of a Barbarossa scenario -- German units will disengage FORWARDS during the blitz phase into hexes that became friendly earlier in the turn.
...does the zone of Control cross a river when we are in winter time and the river is frozen?
No, ZOC do not extend across rivers (whether or not they are frozen).