All official questions about either the FVC or the FRC games should be posted to the
Official FIRST Forums for the official answers; all answers posted are "unofficial".
That said, here are the "unofficial" answers to your questions.
Can we use wood for VEX?
No. Only official Vex Robotics parts or additional parts from VexLABS (with the exception of the pneumatics) are legal as per <R5>.
Also, can we enter 2 championship events?
You can legally enter as many as you want, however you are only eligible to win awards at the first two you attend.
As well, can we change our vex robot between the GTA and the Penn championships?
Yes. There are no restrictions regarding changing or modifying your FVC robot between competitions.