I don't think it matters whether or not you dispute online or by paper. The CB's are required to respond either way. At least if you do it online, you have immediate confirmation of the dispute. That's what I would personally do, but if others found writing more beneficial, please let us know.
Mortgage pulls should not affect your score tremendously, just a point or two and I believe if they are all run within the same 2 - 4 week period it counts as 1 pull. I know it does not have the same effect as trying for credit cards, but I can not say with certainty how many points these pulls drop your score.
It's hard to say whether getting a new open line of credit will help or hurt your score as far as a mortgage goes. Mortgages depend upon so many factors, that it is impossible to say what effect one new open trade line will have. It depends upon usage on the card. Other factors that come in to play for a mortgage are not only your credit score, but also your total debt to income ratio, your loan to value ratio, length of credit, types of credit...A 600 score is almost good enough for prime and depending upon the other factors, you may get a decent rate offer.
Good luck. It sounds as though you are off to a great start...
