you can enable online and connect the console to eshop.
You don't need to actually connect to eshop to update the console, you can go to settings>update.
The current latest version is the requirement for all hacks (v5.5.1).
After you updated to 5.5.1, you might want to block future released updates (not sure if there will be any, it's just a protection) by setting Tubehax DNS or another server blocking method.
Haxchi is not really blocked, more like "not compatible" on old firmware versions.
it works on all 5.5.1 regions (JPN/EUR/USA)
the homebrew launcher only launches homebrew.
There is a "WiiU backup loader" called loadiine to load games from SD card.
Loadiine might be updated to work with USB (that's only an hypothesis from me ! don't take it for granted)
Other homebrew are not really used to "load anything to be played".
Instead, there is a homebrew used to install official game's dumps to the WiiU, instead of using a backup loader you just use the console to launch the game like if it was a legitimately bought game from eShop.
But some games will require signature check function to be patched, this is where Haxchi and CBHC come into play.
not ALL games installed to the console need signature check or Custom Firmware, only the "eShop only" games. it means all games which exist in disc format are fine. All games which exists only in digital format will require signature check (because they are tied to the console used to buy that game, while disc are working on ALL consoles).
additionally, the patcher is also patching the game's region, so it's useful if a game disc is only available on japan but you want to play it on your USA console.