When my mechanic tried to adjust the air intake valve was stuck. Replace it?

What is your question?

My battery keeps being drained by things staying on after car is turned off. Ie. Lights shut off and radio 📻 comes on. Heat comes on when car turned off. Every time door is opened must switch lights on then off, etc. When I start car it dies immediately . It runs only with foot on gas and brake at same time and car shakes. If you take your foot off gas it dies.

What makes this problem better or worse?

Worse when you go slower as car shakes

How long has your 2003 Cadillac DeVille had this problem?

3 days and 2 jumpstarts