Are there many Namecoin domains in use? I know that the idea of namecoin is to create distributed DNS system.
I also know that one can by bit address with namecoin.

But I have never seen any bit domains. If they do exist, how reliable are they?
.bit domains are not recognized by ICANN, the company that runs the main internet DNS. This means that most operating systems have no support for them built-in.

So, to be able to visit .bit domains, you will have to do some configuration first. You basically need to let your computer know where to search for the IP address translation of the .bit domain, as most computers head over to ICANN's DNS servers for doing that.

Considering the reliability of the network, that's not easy to measure. I'd suggest you look at the number of clients connected to the Namecoin network (I cannot find a reference for that.) and the amount and speed of the available DNS proxies. On the page I just mentioned, you can see that a decent number of DNS proxies exist for Namecoin. I have no experience with using them. Considering you choose one that is close to your physical location, I'd guess they are fast enough.

On the amount of available domains, I think the .bit TLD is not quite adopted yet. But you can see on the Namecoin explorer page that new addresses are added at a fast pace. Here you can find a list with some popular .bit addresses.