Yours is a very detailed post, which I'll address a few main areas:
- the number of hours that baby sleeps means by the time she falls asleep until the time she wakes up for a feed. In your case: 9.30pm - 4.30am means 7hours. Baby is considered sleeping through the night if they sleep for 5hrs until a feed. Congrats!
- it is almost impossible to 'drag' your baby's feed, when she is already hungry. Just feed her at 6-7pm if she needs milk.
- try offering some milk before baby falls asleep at 9.30pm, so that she goes to bed full and may wake up later. Even if she drank at 7pm, try feeding her again at 9+pm.
- learn 'dream feeding': if baby doesn't wish to take the 9+pm feed, let her sleep. When she is asleep and before you sleep, give her a 'dream feed'. This means when she is soundly asleep, carry her gently and tickle her lower lip a bit with nipple or bottle teat. She may open her mouth and you can slide in the nipple/teat to feed her while she's sleeping. Usually very little air is swallowed in a dream breastfeed, so burp the baby gently. It is possible that there is no gas to burp. Put her back to her bed and she may continue sleeping till morning.
- dont't expect baby to live according to a predictable schedule cos you may be disappointed. As she grows, the number of hours she can stay awake lengthens, her appetite increases, so her schedule will keep moving. E.g. My 11-month old boy has changed from taking 4 to 3 to 2 naps. His feeds has adjusted according to nap-times, his appetite also gradually increased to taking 3 meals a day on top of milk feeds.
You may have an estimate schedule, give baby + or - 30-60 min around it.
Hope the above helps.