Is there any way to connect my iPhone to the internet through my MacBook Pro?
Sharing wifi to your phone is a piece of cake. Your computer just can't bridge a network. Go to System Preferences -> Sharing and enable the network. Then connect to it from your iPhone. 

Traveling on an airplane would not affect the performance of your computer's wifi, and yes, at least in the U.S., you are allowed to do that above 10,000' feet (although I've never seen them enforce it below). 

The FAA has changed rules within the past years that require devices to be on airplane mode (no antennas activated) while below 10,000' but that isn't necessary above. Many airlines actually provide wifi onboard (like many Southwest and some Delta aircraft).