They do in the UK: you can bring a pen if you want, but you should probably make sure it's something which quick drying ink so it's not likely to mark other parts of the ballot when its folded. In terms of tampering with the ballots it really doesn't make much difference: there are ways which are far easier to pull off and harder to detect to tamper with them than erasing pencil marks, and the way the election system is designed to protect against those ways also effectively prevents any issue with what was used to mark the ballots.

They do, in the UK. Supposedly this is due to the possibility of pens containing disappearing ink. More likely this is to avoid ink being accidentally smeared across the ballot, since it has to be folded.

Why?