If it will make the same squeal turning full locked to the left as well, I might think the serpentine belt is worn and/or loose. If you think it might be at the wheels or in the suspension, I’d want to look for a severely worn wheel bearing. If they’re effed bad enough, they can sometimes make odd noises you didn’t know they could. Then it’s a matter of getting the vehicle up in the air to do a good visual inspection. Look for evidence of something rubbing on something else in the wheel wells. Even the dust shields should be looked at. Nothing should be rubbing on anything.
A stream of water on your floor mat would be an indicator that the drain for your AC evaporator is likely plugged up. Water condensation and runoff is normal with AC operation, but it should be able to drain out in the engine compartment and not on your floorboards.