This seems like one of those things that sound right on a macro level, but doesn't take into account the inelastic demand of travel. For it to actually reduce emissions (the goal), the tax would probably need to be much, much higher to the point where you just don't go to grandma's funeral.
Honestly, for me, the TSA and the actual flight experience in the US as kept me from flying at all since about 2006. I can't stand any part of it. I don't care much for driving either and only put around 2000 miles a year on my vehicle. Most of this is because I can work at home. I guess I've got a pretty low footprint.
Nah, you just need enough pressure to move people onto electric cars.
A plane might be one of the last holdouts on fossil fuels, but even then renewable fuel shouldn't be that expensive in bulk.