Last question is outta my territory. To the best of my knowledge it should help a little bit especially if you have no other installment loans on your credit, it show that you are making a healthy credit mix. Be aware that it may drop you a few points, short-term, for the inquiry but as far as long-term is concerned, it should help.
Now onto what I do know: COSIGNING IS A BAD IDEA! I had an ex girlfriend bounce on a car and got it repossessed. A cosigned account is just the same as any other account in your name. IT'S WORSE! IT SCREWS TWO PEOPLE'S CREDIT REPORTS AND NOT JUST ONE. I got the repo of mine though, had to twist some arms. I love the lady that worked with me over at the creditor. She did all she could to take it off mine but insisted on keeping it on my ex's credit. Ahhh ... I love vindictive you-know-whats.
