Fuse #7, down right.;)
yes
use the cigarette lighter as as a socket
Yes, you can do this.
The cigarette sockets 12v + is touching the earth when you insert the lighter or any other 12v socket. Causing a short circuit, You can replace the fitting very easily for a few £'s/$'s
Use your 12V plug.
no 5v
Yes
The fuse that controls the 12V outlets in the front of a 2004 Beetle will be coded with a title that resembles the words, cigarette lighter. They might also be coded as 12v outlet.
You can replace a battery with a battery of the same voltage but greater capacity as long as it will physically fit.
Fuse box is located on the right bottom side wall near the passenger front seat. Two screws to open the side wall box. There will be a drawing on the cover to show you which fuse. I think it is fuse #6.
No, the replacement adapter has to be of an equal or greater value but never lower.