The website is down anyway. I am pretty sure it needs to be online to have every private key. This is definitely not a big threat, why did you even think it was? Was the site working when you saw it?
No. It would take billion of years to check or browse every private key. This site doesn't have every key on hard disk because it's to much. It's generated on the fly.
There are too many private keys in the world, I doubt this website has even one-quarter of the private keys.
There are private keys generated every single day. There is no chance this website can be keeping up with this.