Until it is signed by both parties, you had no agreement. You had, at best (putting aside an argument of "mistake"), an offer that was not accepted. Landlord has the right to change the offer as long as you had not both agreed on the original. You signing the first with knowledge of the second will not work.
Although a formal retainer agreement is always desirable, it's probably not required for this deal, so not being signed may not be useful to you - how much was the fixed fee and how much was pre-paid?
Ethically, a NY attorney is not entitled to retain a fee for work he has not completed, so really there's no such thing as a "non-refundable" retainer fee. Likely, as you pointed out, some work has been performed, and I cannot tell you whether and what that work was worth or what that...
There are two components to a "mortgage." A promissory note, which evidences the personal debt (like an IOU) and the mortgage, which secures the promise to repay with the property as collateral. As long as the mortgage matches title (you sign the mortgage), you can have your new husband sign alongside you on the note as a co-borrower. This way his credit can help you get a better rate. Most institutional lenders will be perfectly fine with this.
Are they billing you at the new rate or are they just letting you know about the change? The original contract probably gave them the right to change fees, but you need to look at that. you are correct, they are bound by the existing contract.
Absent express language to the contrary, your roommate and you would normally be "jointly and severally" liable for the rent, which means (as the others have pointed out) that you can be charged for the entire rent and it would be up to you to seek reimbursement from the roommate. The landlord won't have to hunt for anyone as long as you're still there.