Hi Robin I think we use 'mend' less than we used to. I wouldn't mend a car or lamp, but I might mend clothes or shoes. But I could just as easily fix or repair them instead - and probably would, nowadays. There's a British phrase, make do and mend, that you might come across. It means putting up with, and if necessary repairing, what you have rather than buying something new.

American English - It is not used other than in expressions. We would say "to mend fences" (to make up with someone) or "on the mend" (recovering) but I can't think of any daily use for it.

US and British usage tend to overlap a lot, more than people sometimes think. In US English, it is much more common to say "fix" or "repair" than "mend." In US English, "mend" is mostly used in a narrow context. We mend something that is torn. For example, we mend a tear in a piece of cloth or paper. For example, a popular brand of sticky tape is called "Scotch Magic Mending Tape." There is a specific idiom used in US English. I don't know if it's used in the UK. It is "to mend fences." By custom, maintain the fence that separates two pieces of land is the joint responsibility of the two landowners. So "mending fences" suggests "cooperation between neighbors." We use it to me "to try to mend a personal relationship that has gone bad." For example, "So-and-so got angry at me yesterday. I'm need to mend fences with them. I'm going to apologize and offer to buy them lunch."

You can confirm what everyone has said already by using the Google NGram viewer, which shows that "fix" and "repair" are much more common than mend ... and have been for a long time.