1) It's perfectly fine to turn off normally. The option in HBC is just there for convenience (e.g. if you're using a GC controller and want to power off without getting up etc.)
2) BootMii inserts itself in the boot process of the Wii. In other words, it gets loaded before the System Menu (the main Wii interface). Within BootMii, you can do a few things. The main feature is it's ability to backup and restore your NAND. In essence, what this means is that it takes a snapshot of the exact condition of your Wii's internal memory, which can then be restored at a later stage if required.
A few things to note about this; if you brick, this is a sure fire way to recover. However, you will lose any and all other changes made to your Wii in the time between taking the NAND backup (or NAND dump, as it's also known) and restoring it. So any updated save games or newly downloaded VC or WW titles will be lost. If you take regular backups, and always take a backup before anything "risky", you can avoid losing much/anything.
BootMii will (by default) load it's own menu when you power on your Wii, but once you've made a NAND backup you can set it to autoboot the System Menu (or HBC, if you'd prefer) so it doesn't get in the way during boot. Also, because of how it works, you can't use Wii remotes within the BootMii menu, you need to either use a GC controller or navigate using the power and reset buttons on the Wii itself.
3) Generally, stay away from anything that modifies the system in any way. Stuff like IOS patchers, cIOS, theming, anything mentioning "patching"; these are all things which can potentially be dangerous if you don't know what you're doing. If you think you need to use stuff like this, make sure you know exactly what it does, why you need it and how to do it properly. Most of this stuff is only really used for backups & piracy (mostly piracy), and as such is against the rules of discussion here.