I keep getting gross foods from the Tombola, and I kind of don't want them to go to waste. Will anything bad happen if I feed them to my neopets (do they get sick/unhappy/weaker)?
No, I know for sure they wont get any disease or lower any stats. I dont even think they will get unhappy. You might get an unhappy response from your pet when you feed it... but I don't believe it will lower its happiness level at all.
Nothing will happen, food is just food no matter what type or what shop it stocks in. Your pet could say it dosent like it but food is food. It will not refuse food either.
They won't like it, but probably not a disease or stuff like that. Your pets will take mostly gross foods
I'm pretty sure their happiness decreases. I fed very rotten tomatoes constantly, and it did decrease. However, happiness doesn't count for much, if anything at all. Do you have many pets? The daily freebies from the omelette and jelly should be enough for them, so the gross foods would go to waste anyway. If you really don't want them to go to waste, sell them for however many nps they're worth. I just donate them.