Hmmmm, there seems to be a lot going on here.
A couple of things - by 8 months she really should be on two naps, even if they are short. They get to a point where a catnap causes more problems than it solves, and can actually lead to shorter naps because they are not consolidating their sleep, iyswim. Secondly, if she only naps 30 minutes for her first nap then you should probably be bringing the second nap forward. For example, my ds sleeps 9-9.30 and is then ready for his second nap at 12 - if I push him much later than that then I get a very short ot nap. Are you able to ap her back to sleep if she wakes after 30 minutes for the second nap? If you do end up with 2 short naps, then you would need to bring bedtime way forward to keep a lid on the ot.
Re the feeding to sleep, last night would suggest that she was genuinely hungry when she woke at 9.45 and that is why she managed a longer sleep after she had been fed. I think it is reasonable to expect that she only needs a maximum of one feed overnight by this age, so perhaps you can feed her the first time she wakes but then find another way to get her back to sleep if she wakes again in the night - even if you are not feeding her all the way to being asleep, she will be getting used to sleeping with a full tummy so she might be waking because she is not full, not because she is hungry, iyswim. You could try giving her some water instead of a bf. When my girls were this age, I seem to remember I used to split their last feed to get them to take more (it never worked for my ds, though!) and if they had a really good feed at 5.30 and 6.30 then they slept better.