Background checks from _public_ records are perfectly legal, if you've got access to databases for that. I do it all the time. The key here is that the information is _public_, and your legal history, for example, can be obtained by anyone with such access, or by a visit to your local courthouse.
Nothing you've described is a "credit check."
This isn't an IP question so I'm re-classifying it.
Avvo doesn't pay us for these responses, and I'm not your lawyer just because I answer this question or respond to any follow-up comments. If you want to hire me, please contact me. Otherwise, please don't expect a further response. We need an actual written agreement to form an attorney-client relationship. I'm only licensed in CA and you shouldn't rely on this answer, since each state has different laws, each situation is fact specific, and it's impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.