Should rabbits eat vegetables and fruits every day?

Some vegetables are good for daily consumption: leafy greens mostly, like Romaine lettuce, basil, and carrot tops (greens only). Otherwise, no, rabbits shouldn't really eat fruits and veggies every day because most veggies (including carrot) and all fruits are too sugary or full of carbs and so they're only good as a treat for rabbits. One or two small bites of treat food every few days is enough!

If a bunny eats too many treats, his appetite for hay will be spoiled, but rabbits need to eat lots and lots of hay every day to keep their teeth and guts and emotions healthy. Also, a sugar spike can lead to G.I. stasis (a painful and even life threatening condition). Too many treats over time can lead to obesity, which causes a variety of health problems. Too many treats can also lead to diarrea or cecal dysbiOSis, which again can turn life-threatening.

See the related question below for more details about the rabbit diet.