[Halcyon]

Yes.
It is fine to leave them plugged in.

Your best bet with new equipment is just to test it out a while in case it did malfunction, but once you are happy it is working fine, then you can leave it on.

Just make sure you obviously don't put things on top of it so it can breathe. They can get hot.
Also, make sure you don't overload wall sockets using too many extension cables, etc.
All this is fairly standard stuff.