The countries in the main arena (late, mid, and early war) aren't divided into axis or allies the entire plane set is more or less available to each country. Once your in the tower you need to open the clipboard (ESC) and go to the hangar to select plane and load out (guns, fuel, ordnance). You'll see a cluster of buttons in the lower left corner of the clipboard with an "H" in the middle this is the spawn direction on the runway. "H" means hangar and the other buttons correspond to a compass heading. If you couldn't spawn a plane there were likely one of three things happening.
A) you were at the vehicle base or port - you can tell by looking at the clipboard map airfield are A##, Vehicle bases or "V-bases" start with V, and Ports a "P". Airfields can spawn planes, vehicles, and sometimes PT-boats. V-bases can only spawn vehicles and sometimes boats, Ports are the spawn locations of the various CV (Carrier) groups that roam the map and you can spawn Vehicles and PT boats.
B) the hangars had been recently destroyed. The opposing side can close down a field by bombing and destroying the Fighter, Bomber, of Vehicle hangars which make it impossible to use that type of craft till they respawn (about 15 minutes IIRC).
C) you were trying to fly a "perk" plane - a small number of aircraft and vehicles have a point cost associated with them. They are usually late war machines of high performance and the cost is meant to keep them from being over used. You earn these perk points by achieving certain things in game.
I highly recommend you visit the Trainers website
http://trainers.hitechcreations.com/This should answer a lot of the basic questions for you.