Volkwagen Beetle Electric Issues?

The beeping for 10 minutes is a warning bell. Something is WRONG.  Shut off the engine on the side of the road or in the driveway...I would not LEAVE THE YARD until this is found out, wait about 3 minutes and pull out the oil DIPSTICK AND SEE IF THERE IS ANY OIL ON IT.   You are "Way past the IDIOT LIGHT WARNING" when you get the beeper or buzzer.

EHHHH DON'T RUN THE ENGINE!  It is on the path to self destruction.

The headlights are a separate issue...that has its own problem that is not OIL related.

See a mechanic and have the car towed there.  If you can't figure it out.  He can.

10 minutes is a really long time

2 minutes is a really long time

1 minute is a really long time

15 SECONDS IS A really long time.

THE WARNING SHOULD NOT GO OFF EVER.

(note,,,I am not yelling, I am trying to highlight it as being "important"

18 year old car - then I am guessing water is getting into the fusebox from the wheel well.   They made a weld mark there and that metal rusts faster so water from the tire is splashed up against the firewall which is the back of the fusebox.   First disconnect the battery(if you are going to do this work yourself.)  Now use a Philips screwdriver(or 8mm socket) and unscrew the fuse box from the firewall. Leave all the wires connected.  You want to see the back of the fuse box.   If it is full of dust(that is what you want to see).  If it is clean and a little rusty, then the water is coming through the wheelwell and splashing onto the electrical.  Road water has salts in it and that is like a wire so it shorts out across the fuse box. Some things work and some do not.  If the copper in the back is green, that is moisture.  The fusebox can still be used but you are going to have to disconnect clean the fuse box tang and wire connection and reassemble one wire at a time.  Another fuse box is over $100 (I am cheap and got time on my hands).  Might as well take out the driver's seat so you have more room  to lay down and do this job. (or you can pay a shop to do it for you for $600 - yeah as much as a motor job.  They will be doing the same job I am telling you.  Hopefully you got a garage or back yard and a canvas tent(a mini shop) to work in as this not fun.   While the fusebox is off the wall and you want other things to do, you want to pull the carpet off the firewall as it is glued there.  Get it right to the floorboards and you may find that the cushion underlay is soaking wet .  Your car smells damp because it is damp.  As you took the seat out you can feel that the underlay is wet .  Drag it out and hang someplace so it can dry in the sun. Which may take 2 days.

 Now, I seem to remember that the fusebox was held down by a nut because all I can remember was the threads and the rot at the base where it was welded to the firewall.  This is where the leak is coming from, not the window seal.  If your fender has a plastic liner then you would not have this problem but the basic Jetta only has the metal firewall and is coated with undercoating.    I mostly had no wheel well liner but one of them did have a ww liner and that one had no electrical issues.

If you got the standard basic car with no ww liner then all you can do is TAR the heck out of that spot inside the wheel well.

. Now get back to the cleaning of the fusebox of rust, green corrosion and making the connections all good again.   This will take hours.  Plan on it.

. I am working from what I remember in a 1982 Jetta, & 1984Turbo Diesel Rabbit and 1980 Rabbit.   My turbo had the wheel well protection...so fuse box was dusty and carpet underlay was dry.

. You know when the car was first put on the road it did not have electrical problems so there is a reason for it.   The windows going up...I would fault the switch (and you can take them apart and clean them)  If there is moisture in the car chances are good they are either black or green with oxidation instead of shiny copper.  Drying out the flooring helps A LOT.

The Beetle is on a Jetta pan, so the electrical problems would be identical to the Jetta.  That is my expectation.

Have an '03 New Beetle, plastic gear in the window motor shattered.  Got new motor, doesn't work.  The inside skin of the door is also made of plastic and shattered in over a dozen places.

Am thinking about a '17 or '18 Mini Cooper Convertible....

Those are typically low voltage symptoms. The battery may not be fully charging and / or the alternator doesn't have sufficient output. Take it to a shop and have both tested. 

It seems like you need an auto electrician to sort the car out. Start saving.