Take my comments for what they are worth... I don't espouse to be very knowledgeable in this area...
1) When an account is in dispute, it isn't counted in your score. Once the dispute was resolved, the account was factored into your score. It sounds like it is being counted as a new, maxed out installment loan. Maxed out installment loans don't hurt as much as a maxed out revolving line of credit. However, it isn't really a good thing either. Your score will increase as you start to make payments and pay the balance down. See #2 for another possibility.
2) MyFico only triggers on certain events. When it triggers, they calculate your new score. But the trigger may not be what caused your score to change.
Paying down your CC balance normally doesn't cause a point drop. I am sure that the score drop you had was related to something else happening on your credit report. Just keep paying down the balance and your score will increase.
Side note: The main exception to paying off your CC's, is if you pay off everything, then your score will drop. You want at least one CC to report a balance. That is not the same as carrying a balance each month.
3) As long as the dates are close, I would NOT worry about this. Next month the old accounts may be deleted completely from your credit report. Or they may not be. This can happen when accounts are sold.
Just keep paying as much as you can towards your high interest loans, never pay late and your scores will increase over time. Rather than concentrate too much on your scores, I would try to focus on your credit reports. If the data is all good, your score will be where it needs to be when you are ready to buy a house. Talk with your partner to ensure their report is also where it needs to be. Both of your scores need to be "good".
The biggest challenge for most people just out of school with student loans is getting past the DTI hurdle. Unless the two of you are making very good money, it can be difficult to save enough in a couple of years for the down payment and cushion for buying a house. All the while paying off your student and credit card loans. It can just take more time to acquire the needed savings than it takes time to increase your credit score.
PS. I know there may not be much left after paying bills and saving for your down payment. But if you have access to 401k with a match, please take advantage of it, It is free money. Plus most 401k's allow loans. You will still need an emergency fund, but having a 401k as a backstop, reduces the need for a big emergency fund.
Good luck!
EDIT: Corrected typo in #3
