I installed a ceiling fan but there’s something wrong with the wires that I can’t figure out as it trips the breaker when I turn it on. I connected the green to green, white to white, and black and blue from fan are with black from the house.

Wiring sounds OK. Try removing the fan and checking to make sure there are no exposed wire connections touching something. If that looks okay then try installing a light fixture in its place. If the problem goes away, then there may be a problem with the fan. If not, then you have may have another wiring problem in the circuit somewhere.

I am putting in a GFI circuit for a whirlpool tub, but the wall at the foot of the tub where I need to put the outlet has no space for me to drill a hole to feed the wire. Can I drill a hole in the plywood and run the romex through that hole and then in a pipe to my panel?

It’s acceptable to run Romex® on any other non-metallic sheathed cable through framing members, but it can't be left exposed anywhere (read: subject to damage). Sheathed cable assemblies also can't be run in conduit, although some inspectors will allow an exception for a short piece (usually around 2 feet) to be sleeved in a piece of pipe.

If you have a longer exposed run to make, it might be a better idea to use type MC metal clad cable for the whole run.