Question about expired domain

I will buy expired domain to build money site on it. But i have some questions.

1- the domain is register with Name Bright, but i have acccount with NameSilo. So do i have to make an account on NameBright to register the domain with it or just use my register namesilo. I'm speaking about does it will hurt the domain serp in the long term if I changed the register

2- Aslo about the hosting, does it will hurt if I changed the hosting?

No
No

1 - Registrar doesn't make difference when it comes to SERP. Registrar basically just hold the domain name for you and that is all
2 - You are buying the domain, so you can link it with any hosting available. It won't hurt SERP or anything else either. If you go deeper -> better hosting = in theory better site load time = in theory, better SERP results, but it doesn't have to do anything with the domain

No for both.

No, transferring the domain to another registrar or host won't affect the domain performance is SERP.