Yes, in a divorce a court will seek to divide all assets in a 50%-50% manner. Some deviations are possible. There will be many issues to deal with and so you should find an attorney you trust that you can work with.
It's not clear from your question whether the court awarded you $2,000.00 in attorney's fees or "statutory" attorney's fees which are about $200.00. That is a crucial difference. If you were awarded $2,000 it would be worth seeking relief from the court. If it is for only $200 probably not.
There is no legal definition, it depends upon a number of factors. From what you say, it is a close call but I would say she is a guest. To live somewhere, one would have mail delivered there, spend almost every night there, have a driver's license with that address and have an intent to live there and not have a place of her own. There are other factors, those typically associated with living somewhere. Your roommate does has legitimate concerns. from what you say I could make an argument she...
"It's my understanding that the MSA rules until there is a stip or change in order. "
That is correct. Unless the MSA or Judgment of Divorce makes some provision for a party moving and that having any effect on placement or visitation, the terms of the MSA control regardless of your moving.
Land contracts are different than landlord - tennant situations. Look at the contract and see what it provides for if payments are not made on time. As for evictions, they can happen any time of year but often do not happen the week between Christmas and New Year's Eve. Good luck!
The answer requires an analysis of their Marital settlement Agreement and final judgment. It's hard to say from what you have said but barring access to the house until she starts paying would be one idea. Another is deducting the extra he has been paying from her share of the proceeds when the house is sold. Good luck.