In archlinux, the mythtv database files are located in /var/lib/mysql
If you have mysql's binary logs enabled (in archlinux it is enabled by default, I think), then the binary logs are also located in /var/lib/mysql
Some configuration settings are located in ~/.mythtv
I don't use an infrared remote so I don't know where those files are located.
You can also check http://www.mythtv.org/wiki/Database_Backup_and_Restore
but I have not had success with the scripts on the mythtv wiki even with v0.24
I use archlinux and the upgrade from v0.24.2 to v0.25 went smoothly. No database problems and existing recordings remained in the database. v0.25 handles themes differently so you may get errors when upgrading saying that certain files related to themes already exist and the upgrade will fail. You can move the files elsewhere then continue the upgrade. Alternatively, just delete the theme files. Once upgrade is complete, you will have to select a theme from the new theme chooser accessible from mythfrontend.