Keeping 50 domains UNRELATED.

I'm starting a project that will require about 50 new .COM website names
to be registered and then hosted (cheap, shared) with cpanel and cron, to run a PHP script.
I already understand: don't register & host at the same place.

I want ZERO connection between the 50 websites. Thus:
All the hosted domains should have different IP addresses:
111.22.33.xxx and 111.22.33.yyy is Not OK.
111.22.33.aaa and 111.22.66.bbb is OK. Do you agree?

Questions:
1. Is it a problem if I Register multiple domains at the same registrar?

2. Some host sites can offer different IP numbers as described above.
Is it a problem if I Host multiple sites at the same host service?

Thanks for your input.

BlueWhale27