High pitched howling and screeching (yes two different noises). The howling appears to happen when the air conditioning compressor pulley engages. The screeching, my guess would be from the belt. Any suggestions?

When the AC compressor kicks on, an electrical load is placed on the alternator and the drive belt that turns the alternator pulley, if not tight enough, can cause the belt to squeal. Replacing the belt should help with that noise if the belt is stretched from wear. The screeching noise can be from a bad idler pulley, a bad belt tensioner pulley or a bad alternator pulley or a failing clutch on a very old ac compressor and rarely a water pump pulley. To check pulleys remove the drive belt and turn them individually to see if they can be tilted up down or sideways with play in the "bearing" of the pulley. Also, you may wish to visually inspect the clutch on the ac and look for melted black rubber around the bolts that secure the clutch to the compressor (stinks,smokes and melts these rubber areas if ac compressor clutch fails).

First, with engine off, check condition of belts. Are they dry & cracked where they ride on pullleys? If so need new belt. Also carefully while engine on look at belt & see if wobbling or slipping. Most likely need belt tensioner &/or idler pulley.