There is a schreeching noise after starting and occasionally while driving

When I start my truck, there is a high pitch noise that last for a few seconds then stop. I comes and goes while driving. It sounds like when you try to start your vehicle after it is running and the starter gives that screeching sound. I recently replace the starter with a new one and fan belt, water pump and tension pulley.

Another problem is with idling. When in park, it idles great. Once I shift it in drive, it rumbles and vibrates like crazy. It goes away after I start to drive but quickly returns at stop lights. Help please.