I work in a kitchen where the floors are wet and slippery. Are these a good shoe for those types floors?

This shoes are not water resistant, but they sure have some sort of material that will make it difficult for water or any liquid get to your sock as fast as a regular shoe. They are slip resistant, oil resistant and the most comfortable shoes I've ever own for restaurant service. I work in the kitchen 5 days per week around 10+ hours. I've scrubbed floors, drop eggs on them, stepped in mud, and they continue to deliver. The only problem is that they run out really quick, I'm buying my second pair in 5 months, but they are totally worth it.

Are they laces or bungy style?

Theyre elastic and in a loop no with no ends. I actually replaced them. But shoes are awesome durable and very comfortable. I will definitely buy them again

No it’s very comfy, it’s even better after you add insoles

Do these sneaker, repel water as in whe its raining out?

The shoe by itself is breathable and fabric, so they are NOT waterproof. But if you spray fabric sealer on as I did then they become water resistant (light rain no problem but a soaker my feet get a little wet). I work in foodservice kitchens so these have lasted a year and still comfortable!