It can go either way. It really depends on what the new issuer intends to do with the accounts it acquires.
The good ones are harder to find.
It would be nice if there would be more consistency among scores. There's always going to be cases where your score is one thing with one bureau and completely different with another.
Read the material carefully. If you find it's unfavorable, it's worth a phone call to issuers to tell them you're going to leave if they can't match the old terms.
It's worse to lose your home than to miss a few credit card payments, frankly.
Many people don't realize that hiring a financial planner can be a good investment. If you find yourself letting important financial decisions go because you just don't seem to get around to them, you might want to talk to a financial planner to get those jobs done.