Thank you for your question, Alicia.  You should not remove the leaves until they turn yellow.  They are photosynthesizing carbs which 'renew' what was used by the bulb to produce leaves and the flowers over the winter.  If you remove the foliage, your bulbs will get smaller and weaker, and will not produce flowers.  Yes, bulbs are perennial; they can last for many years.  https://web.extension.illinois.edu/bulbs/bulbbasics.cfm
As for planting vegetables around the bulbs, it is not recommended, since the vegetables will complete with the bulbs for water, nutrients and, while the leaves remain, sunlight.  Both bulbs and vegetables should have their own spaces.  If you grow anything around the bulbs, consider a shallow-rooted ground cover such as the ones suggested here:  https://web.extension.illinois.edu/bulbs/landscaping.cfm

If you want to grow vegetables but have run out of space, you might consider using containers, as described here:  https://today.oregonstate.edu/news/no-room-vegetables-pot-your-plants

Good luck!