I want to register many cheap domains for several months. What are the cheapest TLDs now? I want to use such TLDs for testing online services.

And another question: what problems can there be with such cheap TLDs?

If you really don't care which domain zone to choose, then you can try .cyou for $1.17, or for example .icu. You can check this at Pananames registrar. I have been registering domains only here for a long time, there were no problems.

Yes, the price of registering a domain name suits me. But renewing such a domain would be expensive, right?

Domain renewal prices are known in advance and are determined for 10 years in advance.
In general, I advise you to check my signature and try the Pananames registrar.