96 Mustang V-6 stick shift loud screeching noise when you start it then it comes and goes as you drive?

Usually that noise is caused by a slipping serpentine belt. When you first start, the alternator is creating a lot of extra electrical power to recharge the battery. During that time the alternator is more difficult to turn and if the belt is even slightly loose or the tensioner is marginal, it will make that terrible noise.