Auron,
As others here have suggested, it's always best to install the latest updates. SME6 is still considered beta and even the latest release (beta 3) had issues that the updates will address.
You asked if it's common for these DSL router appliances to provide DNS services, it varies. More advanced ones, particularly those that have internet access logs, will be able to provide name services to your network. Cheaper ones probably won't. If yours does provide these services, it'll be detailed in the user manual.
As for setting your SME server up in server and gateway mode, this lets the SME software become your firewall and provide name services (DNS) and etc to your internal network. Having a cable/DSL router between SME and the internet often times causes more trouble than it's worth. SME is a very good firewall, I've read here that people have been able to crack a DSL router without much effort but SME is much more solid. That's not to say SME is unbreakable, just saying SME is an excellent firewall as well as provide network services. If you set SME up as the gateway in server and gateway mode, most if not all of these DNS issues will go away.
A last alternative may be to add entries into the hosts file on the local PC's. If your clients are Windows, check this path:
C:\WINDOWS\system32\drivers\etc\lmhosts or C:\WINDOWS\system32\drivers\etc\hosts. Check the file named lmhosts.sam (in the same folder) for syntax. I wouldn't recommend this as anytime you create a new domain name, you'll have to update this hosts file on each machine on the local network.
Good luck,
Dave