If you are both listed on the mortgage, then it is in your interest to make sure that the payments are kept up until the house is distributed in ED. You can draft a separation agreement between you which spells out who is primarily responsible for the home (meaning she can agree to assume all of the payments, and you will sign the house over to her once she re-finances for example), but you will want to make sure that the mortgage is caught up in the meantime.
Alimony is totally up to you. You are likely to qualify as a dependent spouse considering the huge differential in your incomes, so you can certainly claim alimony if you wish. You can agree to a set alimony in your separation agreement as well, or you can agree to waive alimony if you choose. If you two cannot agree on an alimony amount in the agreement, you have the option to file for post-separation support (temp. alimony) and alimony at that point. Just make sure you file for ED and support prior to your divorce being finalized, or you will be estopped forever from making said claims. It’s always preferable for two parties to work these issues out on their own in an agreement than to file litigation. Litigation is very expensive, very time consuming and both parties surrender control to a judge on the unsettled issues. Hopefully you can work out an agreement together instead.