Actually speaking of cold food, DD doesn't really like anything warm. We always cool things like pasta, meat or veg in the freezer but she won't eat it if it's still warm. She'll pick it up and then throw it away!

Triplej maybe a highchair would help? We have the ikea one it's great and so cheap and easy to clean. We have another highchair that is more padded but it's a nightmare to clean, especially doing BLS, plus it's a bit big for her so she looks tiny in it.