First of all, welcome to this forum!
When I connect from my laptop to the DD-wrt openvpn server from my internal network to the hostname "my.dynamic.dns.name", which resolves to (say) my.external.ip, I can only "partially" connect, (all the certificate stuff works, and port forwarding 1194 is enabled).
and
When I connect to the openvpn server at address 192.168.1.1 instead of my.external.ip, everything works fine, and i can resolve hosts names and surf the net.
Are basically the same, exept the point where you hit the firewall-rules for the dd-wrt router AND as you expected, the routing issues.
It seems like a routing issue, when I'm connecting from the external ip the vpn does not seem to route correctly or resolve hostnames. Google and man pages aren't helping, any ideas?
In your config i see you are using
redirect gateway
and you are testing from your local lan. This will cause routing-loops and therefore it can block your internet-access.
Besides this, i'll advice you to use
redirect-gateway def1
and test from another internet-connection (ask your neighbours or the local starbucks). It's pretty difficult to detect errors in your routing-tables if the gateway stays the same because you are already in the same lan.
If that all works fine, you could test
redirect-gateway def1 local
from your local lan
For the differences between both options, i'll advise you to read the section in
manpage for redirecting gateways.
Hope this helps.