1st problem: parking lights and interior lights are turning on and off. But my headlights are working ok. the fuse and battery is ok.
2nd problem: engine is not rotating when starting. alt and starter is brand new. thaen when it finally starts it running really rich.

 

parking and interior lights = sidemarker and signals, and dash/HVAC lighting, correct? - if so, you may have a faulty headlight switch.

"engine not rotating when starting" explain that, because if its starting, its damn sure rotating.

You may want to try a fresh battery or check your connections at the battery and at the starter first.