Do you need to pull a permit to replace an electrical panel and to change out an AC unit? Or is it enough to have a licensed contractor?

I would definitely get a qualified contractor who would also pull the required permits. Our utility company will not restore power to a new panel without a permit being inspected & signed off.

Some years ago our neighbor in Palm Harbor decided to repair his own HAVC & it caught fire, causing a LOT of damage to the home.

Like us he had also cancelled his insurance a year earlier, as our premiums had tripled after a severe wind storm & a lot of n/hood roof damage. He just sold it 'as is' & moved to Crystal Springs.