The worst thing they can eat is the granola-type food they sell at pet shops and garden centres. (on bunspace you can put their fav food and one bun has "toast" - not healthy!) They should not have too many sweet things or treats and they need fresh water at all times. In hot weather, they need extra water and we put extra bowls in the house as well as of course the outside runs.
We highly recommend the hay and fresh greens diet link to hay and greens diet
Gut stasis is when a rabbit stops eating. They do not eat 24 hours a day but do eat quite often. If a rabbit goes into gut stasis, it is very serious and you should rush the bun to the vet. Their digestive system must be working or they will die. Diarrhea is also a sign of trouble and if it does not clear up after one go, you should also take your rabbit to a rabbit knowledgeable vet.
We do not necessarily feed them fresh veg every day because of availablilty, but remember the most important food is hay. A good quality hay too, not dusty hay fill of seeds. You can find this by the bale, ask around or inspect the hay before paying. Ours is readily available to the buns in large boxes and bowls or hanging feeders that hold about a shoebox or two full of hay - not those tiny dinky things they sell at pet shops. Even if you stuff it in a box and cut a hole in the box for the bun to stick his/her head in and eat, this is a good dispenser. If you want something fancy, you can order something off the Net like this one from Saveabunny.
HAY: In addition to pellets, we use loads and loads of good quality farm hay (and straw, about 1/4 straw and 3/4 hay) we buy by the bale, it is a good value but make sure you get quality hay, not rubbish hay full of seeds and other detritus. They eat the hay in the litter boxes and also for the buns who prefer small litter boxes, they have an extra hay box to eat from. I put fresh hay on the top of the other hay every other day, sometimes daily, and always there is about 6 inches of hay and straw in the box.
Here are some links with good information on what to feed your buns:
bunny herbs to buy online, all profits which support rabbit rescue in Poland: http://ti-vo.pl/index.php?id=2