well the main question is, once you buy a custom character. can you move around the endorsements once bought?
Yep. You change change the endorsements or even the class whenever you have access to the locker room.
You can however have two, or more, custom classes using the same Pro but with a different endorsement setup. So whenever needed you can switch to that other setup.
And whatever skills you upgrade for one pro class setup will be unlocked for the same pro class with a different endorsement loadout. For example, if you have an Assault with Armor/Accuracy/Rate of Fire and upgrade all your skills to level 3, you can switch to an Assault with Juice/Speed/Crit and all your skills will still be level 3. If you switch to a different class, the skills will be L1 until you switch back to an Assault class.
Yep. If you upgrade Tank A and switch to Tank B you keep all your upgrades. Switching classes doesn't keep upgrades, well because it's a different class.