I personally wouldn't stress too much about how much solids she's eating at this stage. Milk is still the primary source of nutrition and food is for tasting and a little topping up. Sounds like you're doing fine. She maybe does associate the booster for play (we also only use boosters but I guess I never used it for activity time), but just continue as you are but perhaps use the booster less for activity time and solely for eating. Just continue what you're doing with offering food and if she's hungry she will have a nibble. It's just about setting up routine, but don't stress over the volume. I also don't think it's necessary to switch milk and solids yet just to get her to eat them, in NZ we're not advised to switch until 9mthsish, so I wouldn't worry about it (in fact I still do milk first at 11mths).
I think a lot of it will be developmental, being nosey, other interesting things she'd rather be doing etc. Just be guided by your dd and let her continue to enjoy meal times rather than it become a boring chore. When she's really hungry she'll eat.
Also with wanting bottles sooner than 4hrs, I'd just go with it, once food is introduced I personally don't worry about feed times so much - I felt as long as I fitted in the 4 milk feeds a day and offer the solids in between it didn't really matter when it all happened - so they're actually eating more regularly than before solids were introduced.
HTH