My bank (Santander), took maintenance and tax credits into account and just wanted 3 months bank statements as proof that it was going in regularly. Not all maintenance is court ordered, my solicitor told me that.
My friend's XH signed a deed of transfer to show that he no longer had a claim on the house, although the mortgage remained in joint names, with the transfer deed held by the mortgage company. That meant that he had no claim on the house even though it was still a joint mortgage.
Re: maintenance, if you have an arrangement through the court or CSA, some banks will take it into account, but pods only 60%.
Re: his name on the mortgage, you are both equally and jointly liable for any arrears or mortgage payments, you are financially linked (if he were declared bankrupt, they could potentially seize your house!), plus he would be unlikely to be able to get a mortgage on another property due to his risk profile.
You can remove his name via a Transfer of Mortgage Equity, but you have to satisfy the bank that you are a good candidate to lend to ie via multiples of your income.
I hope this helps - sorry its not overly positive info!