You can apply for one parent family payment - the CWO who's dealing with your SWA payment can advise you. The Domiciliary Care Allowance isn't counted as means, and you should keep your half-rate carer's allowance too.
Regarding assistance with the mortgage, entitlement is based on the interest portion of your repayment and household income. The offset you heard about is most likely relating to Maintenance - where the first €95.23 is assessed as means, any maintenance over that amount is only partially assessed. As you've said maintenance isn't in payment, it doesn't apply in your case. Again, ask the CWO for advice and application forms.