It seems legit some tested it from one of the trusted members here on the forum.
That doesn't mean anything for the long-term, though. We've all seen exchanges that started out life legitimate and then ended up pulling an exit scam, usually in the form of "we got hacked!".
I'd be suspicious of any exchange that promises that they'll never require KYC, because that's not a promise any of them can really make right now. I'm sure Coinbase, Bittrex, Kraken, and all the other exchanges that require it would love it if they didn't have to because then they'd be able to attract more customers. The fact is that they
have to abide by KYC regulations in order to be compliant with the regulations of the countries in which they operate.
Unregulated exchanges are sketchy at best, and that's unfortunate but true. I'd be careful with this basefex one if I were you, OP. At the very least, withdraw your coins whenever you're done with your trading for the day.