i don't think it wll be easy or cheap for him to adopt her, he's her stepfather so why adopt ? you can change her surname by deed poll when she is here..i'm not sure you can change her birth cert even if he does adopt her.
http://www.ukdps.co.uk/CanIChangeMyChildrensNames.html
yes mention in your visa app and his letter of support that once your settled in the uk and your daughter has finished grade school, you intend to apply for settlement for your daughter and for her to live permanently with you.
also while your in the uk, your mother will be taking care of her, but you will still be financially responsible for your daughter as you will be making monthly money transfers to your mom to pay for your daughters needs (do this and keep the money transfers receipts, pnb are good for this, as you will need them when you apply for a visa for her)
photo copy your visa app and his letter of support, even better if you can scan it, and when it comes to applying for a visa for your daughter ,you can send a copy showing that when you applied for your visa you intended to bring your daughter to the uk, once you was settled.. just minimizing any chance of refusal..
you need to show you have 'sole responsibility' for the child, but from what you said you should be ok on that.