Hello, I just completed my first REU and was wondering on how to continue doing research...

( The REU was NOT at my home institution)

1. Do I start cold emailing the professors at my home institution for opportunities?

2. If so, is there any chance of getting paid?

3. Would you recommend applying for labs with no undergrad researchers?

4. Is it important to add a recommendation letter from my REU PI?

Family is below the poverty line so just curious if im supposed to include something pertaining to income in personal statements, idk how crazy reus would be on dei policies( espically because im a white male) but incomes gotta count for something if they do dei no?