how do I find out if a trip permit is expired if I have the permit number.

Trip permits issued from the same places that you get your tabs and registration from. Not Here! The permit shows a number, expiration date and other details.

When you get a trip permit, you only pay for how long you want it for i.e you pay for a 5 day trip permit then its only good for 5 days

There usually only good for so many days. And usually have expiration date listed.