the embassy might want to interview your daughter seeing she is 12yrs old and still has contact with him, and also possibly contact the father (others who have gone thru the same situation as you on here will be able to tell you if the father was contacted in their case)

you might have custody under Philippine law, but its the British embassy who is issuing the visa and they dont want to be pig in the middle btw 2 parents fighting over a child, not that you are !, but it happens in some cases, that's why they also ask for evidence of 'sole responsibility' to

yes same form and fee.
yes he needs to write a letter of support for her, or one letter to cover both of you, the same evidence he will supply for you, she will have accommodation without overcrowding, he has finances to support her without recourse to public funds.. etc