Penville,
No, you can't charge (By charging here I mean the special charge attack listed in the combat section of SRD). To charge, you must:
A. See the enemy
At the beginning of your charge move (At the beginning of initiative, basically). You might see someone by the time we get close enough to start rolling initiative and stuff.
B. You must have the
clear path to the target of the charge. You want to jump on/over the cart, that exclude the possibility of charging.
C. Must move at least 10'.
Basically, condition B automatically preclude the possibility of charging here (Unless, of course, you have something else that lets you jump and charge, like Leap Attack Feat, that explicitly let you combine jumping and charging)
As for shooting:
SRD:
You can use ranged weapons while your mount is taking a double move, but at a –4 penalty on the attack roll. You can use ranged weapons while your mount is running (quadruple speed), at a –8 penalty. In either case, you make the attack roll when your mount has completed half its movement. You can make a full attack with a ranged weapon while your mount is moving. Likewise, you can take move actions normally
So if Bigby makes double move to jump on top of the cart, you will be shooting at half point. Not at the top of the cart. If Bigby uses single move to jump on top of the cart, you can shoot from there normally.
-K