Left front tire locks up when weight is applied. Works when both tires are off the ground and free wheeling. Also the brake caliper seems to not release the pressure when the brakes are released.

What does it mean when your tires lock up?

Lock up essentially means that the braking force exceeds the frictional force that is keeping the tire in motion. It isusually caused braking while cornering due to the load transfer in the corner. The weight of the car is mostly onthe outside tires in the corner, so the frictional force onthe inner tire is less.This can be caused by a sticking caliper that is dragging and getting hot, or in some cases I've seen, a malfunction in the ABS system, sometimes caused by an air bubble, though I suspect your caliper simply got stuck and dragged till heat expansion seized the wheel.

It could be a locked brake or a frozen bearing. The car must be moved to an appropriate location for being worked on. this will need a flatbed or a tow truck with the dollies since you can't leave the drive wheels on the ground and you can't leave the stuck wheel on the ground. Remove the tire and wheel.It sounds like you could have a faulty turn signal relay. A relay is a piece of electronics which flashes the light on demand. They are generally cheap and easy to replace, so I would start there. If that doesn't solve it you could have a connectivity problem in the wiring.

Possibly a under inflated tire or a wheel balance weight got knocked off. A wheel alignment shop could repair this for under $100. If tires are balanced try tire rotation by putting the rear wheels on the front and front wheels on the rear. If it pulls to one side during breaking it could be worn out brakes or a leaking brake caliper. check inside of tire sidewalls for brake fluid streaks in the inner sidewall

it could be a flex hose between the caliper and the steel line

sounds like you need new ball joints. jack the front of the car up one side at a time so that the tire is clearly off the ground. once you do that try to push and pull the tire from left to right. if it does move then its your ball joints.

Tie rods, ball joints, control arm...

This has to do with the front brake caliper on the left sticking or the front right is not activating. Remove the front wheels and check the caliper for proper movement and pad wear. Try to rotate the front left and note any heavy resistance. Also check all tires for proper pressure.

I would suspect several things

First have the tires spin balanced - my guess is you have a seperated tire
You could have a brake hanging up on that wheel
Or not making proper contact - thus causing the rust or more correctly not removing the rust
It may also be a wheel bearing

its possible it could be a wheel hub bearing,but it could be a faulty brake caliper or a brake hose,if it pulls when the brake is applied then you have a brake issue

You could be having uneven tires; front-brake dragging; broken or sagging springs. Have your front brakes checked.

The only thing I can think of is something got stuck in the caliper , rock or some other goofy thing.Good luck