Research - in loco parentis - read - acted as a parent.
If you acted as a parent to a child whose parent you were in a relationship with (and they had custody of the child) you may be obligated to pay child support, notwithstanding any existing orders from other parents to pay child support for the same child.
She will have to prove you acted as a parent to the child. The marriage was brief, and it appears the Non-Custodial Parent was involved.
Whether or not you acted as a parent will likely be determined on a number of factors:
did you put yourself out to the public as a parental figure to the child
did you participate in raising the child ie. disciplining, schooling etc.
does the child see you as a parental figure
As for the house, there are some other factors. One factor was that you mentioned she bought the house. Did she own before you got married? You believe there is $50k in equity, but the reality is, you are only entitled to any equity gained DURING the marriage. So if the house was bought for $200k 5 years ago, you married <2years ago and it is now worth $250k, you would be entitled to a portion of the equity from the date you were married to the date of separation.
However, if there other matrimonial assets, you are entitled to equalization of those as well.
This is a very short marriage. Even if there is $50k in equity in the house which you are entitled to 1/2 of, how much in legal fees are you willing to pay to get that $25K (less real estate fees etc as well).
I understand not liking her take it or leave strategy and her attempt to blackmail you with c/s for a step child. I hope she sent that particular note via email as a judge would love to see how she positions her kid as a means of blackmail.
Just ensure any agreement you sign isn't signed while you are under duress like that. Have a clear mind and ensure you get sound legal advise.