I like either one or two because they bring some color into the kitchen. I’d find something durable and preferably washable, though.

I think rugs in kitchens are just a tripping hazard but if you like them then one that is washable probably every 3 days.

Choice #1 or #2. Personally I don't like the others for your kitchen. #2 is my favorite, I love color. #1 also nice. I was thinking a longer rug in that area would be much better rather than such a short little one.

Rugs are fine in the kitchen I.M.O., as long as you clean them once in a while. No offence, but every 3 days would be a bit excessive to me to wash them, unless one is OCD level clean freak. How often to clean them really depends how much you cook and spill/drop. I plan to put a rug in my kitchen when my reno is complete, probably and indoor outdoor washable one under the island, and a smaller longer one in front of the sink area.

No rugs in a kitchen. Not only does it not look good (it draws your eye down to it so now you're looking at the flooring instead of everything else you should be seeing in the space), it's a sanitary and safety issue. It holds dirt and grease and is a tripping and slipping hazard. It looks messy. It's going to look dirty quickly. And lastly there isn't a point to it, it serves no function.