Hi sweetie!
First off, some huge (((hugs)))). It's so easy to let this whole sleep thing get you down. I know when my dd1 was small, I worried so much about her sleep and would get so upset if things weren't "perfect".
I again tried shh pat and PU/pd. I also did check nappy and bonjela in case of teething but in the end offered bottle as I am just so tired. ( I cried throughout this as I felt I was doing the wrong thing by offering the bottle but just needed her to sleep! She took a little while to settle after this. I had to go in at 2.30 and cuddle to settle)
It's ok, I promise. We all do things that we think we "shouldn't" sometimes, but when you're just so tired you'll do anything to get some sleep, and that's ok. Definitely do not beat yourself up over it. My feeling is that it's probably more of an A time thing than a hunger thing as she's not going back to sleep directly after the bottle (generally if it's a huger waking, they'll pass right back out after they eat).
My ds sounds much like your daughter -- needed more A time, but it was so hard to get there! In her case, I think you need to push very gently, just a little bit at a time. Since your first A time is working ok right now, I might leave it and work on that second one. If all you can get is 5 more minutes, then just stick with that for a few days. You can add 5 more minutes to her A time every 3-4 days and that should hopefully stretch it nice and gradual. Keep those 5 minutes as low key as you can. With my ds, we'd have to do some shifting of location -- I'd have to move around the house a bit to keep his interest and to keep him from getting too cranky as we moved towards the end of his A time. We'd generally end up at the end in his room with the lights already low -- just super low key to keep things low stimulation.
When she wakes at night, if you feed, I might try offering just a tiny amount. It doesn't sound like she needs it and it does seem to be messing with her intake during the day. Fruits and vegs are good first foods, I'd honestly just stick to the morning for now, it was what I did with all 3 of mine -- dinner came some weeks later, and lunch didn't happen until a few months later!
Hang in there sweetie, it will be ok!