Actually, it is true that if you have a lot of credit checks, they assume you have been applying for (and getting turned down) for loans or whatever and can ding your credit. But I would think one free credit report would not have a big impact on that.
If you live in a community property state, you may be liable for H's bills, but I believe only the ones before he filed for divorce. At least in my state, that was the case.
Be careful about cancelling cards - you do want to cancel joint cards, but again, cancelling a lot of your own cards can ding your credit rating a little bit.
