Q: Car squealing when turning at startup

Sounds like you might be having two issues. The high pitch noise you hear is most likely caused by a loose belt. Depending on your engine you can have several belts or just one. The squeal sound comes from the belt slipping on a pulley that has a load. The extra load makes it harder to turn. When the belt it tight, this is no problem. When the belt is loose, it just goes over the pulley without turning it. The friction caused by the slipping is what makes the noise you hear. It might be a simple case of just tightening the belt. If it is a single belt system, the automatic tensioner has no mechanical adjustment and will probably need to be replaced. An inspection of the noise will be needed to be conducted in person to properly diagnose the problem.

The A/C being slow to cool is most likely caused by low refrigerant levels. The A/C system is sealed. This means that if the system is low you probably have a leak. Refilling the system is usually necessary for a proper diagnosis. The use of electronic refrigerant detectors or UV dyes is often used to pinpoint the location of the leak. Consider giving YourMechanic a try. They will be able to help you diagnose both of these issues and advise you on appropriate repairs.