Remote Buddy makes no difference between network connections. It is 
available through all network interfaces your computer is connected 
to. So, if you have set up your network so that you can reach your Mac 
from afar you can also reach Remote Buddy's AJAX Remote from afar and 
make use of all of its functionality.

If you have network problems, please consult the FAQ for detailed help 
and a run-down of possible error sources.

Regarding sleep: this is a hen-egg problem. If your Mac is asleep, 
Remote Buddy is - like any other app, too - of course not running. It 
- and a lot of other parts of the system, like network drivers, the 
filesystem, harddrives, etc. - would have to run, though, in order for 
it to be able to sleep your Mac.

As far as I know Mac's have support for wake-on-lan, but this is a 
system-level function and beyond the scope and reach of Remote Buddy. 
I did a quick search on the web and this may or may not be of help:

http://www.macosxhints.com/article.php?story=20020220095929695

Best regards, 
Felix