Two things to sort out: getting baby sleep and method of feeding. I'll explain what I did as we had the exact same predicament:
Night time pattern: always had a bath-change-story-milk-sleep pattern, no particular time, just when dd was tired. I used to feed to sleep.
With this pattern well established, at around 10 months i realised it just wasn't ideal as I was the only one to get her to sleep at night.
So I tweaked it by feeding her before her story, she would then lie with DP who'd do stories(same ones for consistency). Obviously this took a few nights of her getting used to DP, she'd come back for milk, faff around, be half asleep and I'd put her down. But, i tried to keep her awake and pass her back to DP to start another story and get her to sleep, even if this meant cuddling her to sleep.
Perhaps over 3 weeks, she got used to the change in pattern: bath- milk - change - story-bed. She now goes to sleep cuddling on the bed and he then transfers her to the cot.
Obviously not ideal shes going to sleep on him, but as a family, we've moved forward.
Method of feeding: persevere with a sippy cup at meal time. Just a basic one. We were late introducing one really but dd wasn't interested and she is breastfed so no massive need for additional water. But at 10 months I realised she needed to learn how to use one. So, every meal time, a cup was present. I offered water with and without lid and after 2/3 weeks, she took it and can now lift herself (she is 12 months but this is possible from 6/7 months) So just keep offering. She would cup feed (with me holding it) from around 4 months - babies naturally can do this I think.
To put in context, dd still wakes during the night and I feed back to sleep but night times are better and I can go out for a meal with friends and not worry that she'll starve. My next plan is to get her to take milk during the night from DP!
Good luck 