Start problems

Hello.

I know that there are probably already many contributions, which are about starting problems, but I did not find one, which addresses my problem!

I drive an S6 C4 Bj 95. Every time the car was over night I have a lot of problems with the start. He needs rel. long until finally the speedometer reacts and the motor actually starts. mostly I need 2 runs for it:)... if I have the starter rotated so long that it should start the first time the speedometer moves only very to the empty speed. if I need two tries he logically does not go the first time and then at the second start he starts better.
After that, however, I switch to D or R and the speed scratches again. The engine is always about to go out. He doesn't accept gas either. But he doesn't go out, he just falls off extremely, but then catches himself again. After that, he runs normal.
This only occurs when he was standing a little longer (zb over night)
I also have an LPG system in it, but it definitely can't be due to it, because it doesn't react at all with a cold motor and only activates on 30 degrees.
I have asked a bit about it before and I was told that a sleigh between the tank and the gasoline pump always has a certain pressure and it could be the case with me that this sleigh does not hold the pressure and he pulls air the first time he starts to turn on and therefore greases the speed...
Has anyone ever had the problem? and do you still know sensible solutions that I could indicate as tip at a workshop???