would you recommend using on reef or in the ocean?

I use mine for beach running all the time and they work great!! They've also come in handy out tubing the rivers and you never know what you'll step on. Dry pretty quick too, like really quick. I might get hit with a wave while running and 2 min later they are already dry while I'm still running. Highly recommend getting some toe socks though for beach running. If you're just using them in the boat or out swimming in the ocean or lakes though I wouldn't use the toe socks for that. Do NOT recommend using them on ANY reef though as any form of touching the reef will kill it, even with shoes on.

I have flat feet, will these support my feet?

I'm flat footed and been wearing vibrams since 2011. Wear them hiking, walking and running. It took a year to adapted the different styal and streanthin my feet. Now run 12 miles road running in my v-run

What if my feet are wide ? Will these be too narrow?

I sometimes buy wide shoes, sometimes regular, at all depends on the shoes but I assume my feet are wider than average. These fit great and I have no problem with them not being wide enough. I have never needed a wide version of vibrams.

are these authentic vibram or counterfeit?

They are not fake and the only reason the say imported is because the factory and company are not all in the same place so there HQ is in Italy and if they get supplies from the USA to make the shoe the the parts of shoe made from that can say imported. But thees shoes the kso black on black pair are real vibrams for sure