Should I prepare a research statement or cover letter for postdoc ads. with general descriptions?
Nobody here can know about the documents that are required, but typically a job announcement has a contact person. Ask them about such details.

The position sounds similar to many postdoc positions in mathematics - they want someone who can do research, be useful to the university, and co-operate with locals. I would suggest taking a look at what the faculty and PhD students are doing at the moment and trying to find shared interests there. Check out the faculty website, personal webpages and Google scholar profiles - wherever you can find list of publications.

You do not need to be doing precisely the same thing as they do, as long as you can make a case that there might be cross-pollination and that you will be doing good work.

If there is a current line of research they are pursuing, mention that. If you could help them move or expand their research, also mention that. You are not setting anything in stone, but rather trying to figure out possible shared interests with the locals. The details of what you actually do will get decided once you are there, most likely.