Is there a checkbox somewhere I'm missing that would let me connect to my internal network from the outside hostname?
(Router named 'toasty'; port 80 is forwarded to a linux server)
For instance, rather than type 192.168.1.1 when I am at home, it would be nice to be able to access my router through toasty.my.host.name/ (or even just https://toasty/). Similarly, when connecting to my server's web address, it would be more convenient to type my.host.name rather than https://192.168.1.3.
What you are looking for is called "port reflection", and no it is not implemented. It is a hack to the IP stack that can cause issues.
What you should use instead is called "split horizon DNS" and is not a hack, but a best prectice. Go into Services -> DNS Forwarder. Put host: toasty domain: my.host.name IP: 192.168.1.32 and host: toasty domain: local IP: 192.168.1.32 in as two entries. This will allow toasty or toasty.my.host.name to resolve to the internal IP address.
Is there a rule that can be done that can make my.dns.name reference an internal IP address, rather than host.my.dns.name?
I'm hosting a UT2004 server for my friends which lets me download maps from a web server (which in this case is the same box). The web server for this config is specified by DNS name, but my other computer internally can't see the DNS name of the server, and so it can't download maps. (I can, of course, copy them on myself, but it's doubling up on the work, which seems silly.)
My first thought is to put an entry in my gaming rig's HOSTS file that would be "internal.x.y.z my.dns.name", but if there's a way I can set that up on the server, I'd rather do that.