Is it likely that there is a universal remote that will be preprogrammed with my TV's advanced feature remote codes (P-mode, S-mode, etc.)?
might be, if you want to go on the cheap side, look at
www.hifi-remote.com to see if the UEI DB has those codes.
If not, what is the possibility of teaching the universal remote the advanced features when I don't have the original remote to learn from?
only if it is PC programmable and someone has a file you can use
Can universal remote codes be downloaded and programmed into the remote like ringtones for a cell phone?
depends on the remote some of the higher end remotes yes (a config file from a PC) Also some OFA remotes have the possibility of becoming PC programmable, by building or buying a JP1 cable