No answer from me about the online stuff → Don't play online, don't know anything.I'm interested in modding my DSi to add stuff like Twilight Menu++, but I just wanted to ask about whether or not this may affect how the DSi works since I've been reading a lot about this but I'm still confused. Like, will all my physical cartridges still work with no issues? If I played something like my physical copy of Pokemon White could I connect to a fan server with a WPA connection? I'm just curious since I want to be sure I won't accidentally mess anything up and have to figure more stuff out to get my physical games working properly. If using modded menus does affect that, then would it be possible to use the original home menu or something to run the games normally?
Using the guide https://dsi.cfw.guide/ will not mess up anything. Unless you install unlaunch (optional) there is no permanent modification and the DSi starts with the normal menu (TWL++ is opened with the camera exploit Memory Pit).
The guide will add a lot of functionality to your console – not take some away.
Good luck and have fun!