Yeah, peanut butter (which they've finally started calling that--it used to be ground groundnuts, which is just not tasty sounding) is mostly not a thing in the UK. When we lived there, chocolate chip cookies were just catching on--people were having cookie-baking parties and there were trend articles in all the mags.

Biscuits are round, flat things, either sweet or savory. Many of the things that serve the function we give to cookies are very much like our graham crackers, but round and often faced with chocolate. Those are generally referred to as "bikkies" and eaten with tea.

I can't help you on the sponge cake question.