Please note that migrated accounts are not supported just yet.
By default, Minecraft is installed in %appdata%/.minecraft/ directory, if you're having issues with Minecraft or ExtremeLauncher you might want to try deleting (or backing up) files in that directory. Remember that world saves and other Minecraft data could be there, be careful when manually removing files.
If you're getting an "Invalid session" or "Disconnected" error you're trying to log in to an online-mode Minecraft server which requires paid Minecraft account, while you're using an offline-mode account, there's no way around that.
If you're trying to log in to an offline-mode server and you see this error, then you could try changing your Minecraft username.
No, no registration or account is required to use Extreme Launcher.
Skins are tied to Minecraft accounts, offline mode accounts will have default skins. On some servers, skins can be changed using in-game commands.
Yes, mods like OptiFine, Forge, etc. are fully supported.