What about AtomicDEX?
https://atomicdex.io/ I've read a lot of positive feedback about it. I haven't tried doing swaps yet, I'll be trying it out soon.(Since it's in open beta now)
I seriously doubt it
To do an atomic swap, you need wallet software that writes a specific transaction script to make it happen. Unless that website is for such wallet software, then they're just using "DEX" and "atomic swap" for marketing purposes
and if so, they are lying. if the name of the website is a lie, you can't realistically expect that they won't lie about other things too