This completely resonates with me as well I think its normal developmentally.
My daughter is perfectly capable of holding a bottle. She is 15 months and still won't do it. She will literally push the bottle into my hand. What I've realized is that she likes the cozy cuddle time of our early morning and evening bottles that she doesn't want to be bothered with holding it. Her sippys during the day, she is fine with, just not the evening bottle. Just keep offerring and encouraging. And if she doesn't want to hold it. Just hold it for her.
Food- I think every child throws food on the floor, and many try to feed the parents. At least mine did.
I think the key to both is repetition. We would always vocalize things in a positive way reinforcing what is supposed to happen. E.g. Food is for eating, food is for your mouth. When you are finished keep it on your tray. It is easier for us to clean up. Don't you like a clean house. Although this sounds foreign as it is easier to say "no" all the time, the fact is kids will eventually tune out no, and they don't necessarily understand what the expectation is unless it is explained to them. This did take several weeks of consistency in the message, but now she only once in a while throws things on the floor. (It is generally because she doesn't like what is offered) Your little girl is still little. Be patient. She will learn. But in the mean time, your dog may be well-fed a bit longer.
In both of these cases, I think your child is still OK developmentally. Keep encouraging her and keep repeating and one day, all too soon, she will want to be so independant that you're going to wish for the days that you were able to do it for her. Toddler days are right around the corner with "me do, me do". Enjoy these precious moments of dependance while you have them! :) (says the mom whose 15 month old is insistent upon walking herself... no more stroller no more carrying... and she still wants me to hold her bottle at night.) :)