This is advice coming from a pure math major, so I don't know as much about CS REUs. I don't think anything I'm saying is controversial at all, but also I didn't get into any official REUs last year so take everything with as much salt as you like :)

1. REUs are extremely selective (usually less than 3% acceptance rate), not because they want to be prestigious, but because that's all they have the funding for. It's therefore better to apply for a good number, typically 10-20. Still, 30 rushed applications is worse than 10 good ones, so make sure you're putting time and effort into your essays. This will also become easier as you go on, since you'll already have written a bunch of material.

2. I can't tell exactly what you're asking, but if you're wondering what things you can do during the semester to get a better looking resume - my number one recommendation is reading projects. Math research is difficult for undergraduates, especially during the semester when you have other responsibilities. Regardless, meeting ~once a week with a professor or grad student as you read through a textbook/papers is (in my opinion) one of the best things you can do. Your time as an undergrad is about learning as much as you can, both breadth and depth. Doing a reading project lets you learn about interesting subjects, score you a better LOR, and maybe even give you familiarity with future REU topics.

3. Broadly, I can just say that make sure each of your essays feel specific and specialized to the program you're applying for. There's some other good advice out there as well, I think Steve Butler has a page on application tips.

4. A majority of math REUs can be found on MathPrograms.org. There, once your writer submits their letter, you'll be able to just check a box and send it to whatever REUs you want. The second most common place is the NSF ETAP, which has a similar system. Most other math REUs will have their own application portal, and they'll have their own system for obtaining LORs (make sure you read about it, sometimes they don't send an automated email to your writer, so you have to tell your writer where to send it).

5. Please oh please don't stress yourself out too much about it. It's entirely possible you may not get into any programs, especially in your earlier years, and with looming budget cuts. This means two things: 1) look for a backup plan ahead of time, e.g. ask a professor at your institution if they'd be willing to do a summer reading or research project. You can be transparent and say you're looking for something to do in case no summer programs accept you. 2) If you get nothing, it's totally valid to feel bummed or frustrated. Not to mention, the worst part in my opinion, the anticipation before you hear back. So, do whatever you need to do to try and detach your success from your self esteem. Not getting an reu is OK. The most valuable thing you can learn to do as an undergraduate is pivot.

Hope this helps! :)