The miles on my 2004 Mercedes Benz changes from 102000 to 165000 all of the sudden. Why do that happened?

Didn't know I didn't have a gas cap drove with no cap for about a week now check gas cap came on and check engine light?

Trying to replace the headlights cables, can't find screws/bolt to loosen the bottom portion. Can someone send me the schymatic?

Car starts nicely once charged, drives in perfect condition may die by next day never know when the battery a 2 year old tested by AutoZone they stated its in good condition.

Lights flicker on their own as if opening/closing the car with remote (has new batteries)Alarm doesn't work, tried opening the car without the remote or key, checked the 3 different fuse boxes. Even tried by pressing the panic button and nothing seems to trigger it on.

In a nutshell, alarm doesn't work, cant remove headlight to re wire, and haven't been able to figure out what is draining the battery.

Thank you ahead of time for any suggestions.

have to charge battery for a second then it starts up, I notice that the headlight cables have the missing insulator.

Our Battery died, AAA replaced the Battery all ok, but nothing when we went start no cranking at all, is there a reset on this car ??

the bult are good