[Android Q&A, Help & Troubleshooting] shimp208:
To answer your questions:

Samsung Galaxy S

ROM Manager

ROM Manger has been buggy for a while now and can cause a lot of problems on certain devices, I would personally avoid it for the time being. That being said the best way to manage your ROM's (And any other Kernel, or MOD's you may want to flash) is too boot your device into recovery mode by using the key combination described in this post, or by running the following command from ADB on your computer:

adb reboot recovery

Once in recovery, you can flash any ROM that you pushed to your phones sdcard. Make sure to always perform a NANDROID backup of your current setup in recovery mode, before installing a new ROM, Kernel, or other MOD (Such as editing your build.prop file). Also before flashing anything in recovery make sure it is intended for your device and that you read and re-read, and re-read again the instructions on how to properly flash the file.

Nexus 7, and other Google/Nexus devices

OTA (over-the-air) software updates

It is always assumed that any OTA update you apply will break root and that you will have to re-gain root access by re-rooting your device. You can disable OTA updates a couple of different ways. One method is to use an app such as FOTAkill to prevent OTA updates from happening. Another method is to use an app such as Titanium Backup to freeze and disable certain system apps that control OTA updates from being sent and received. Lastly, you can install a custom ROM to prevent OTA updates from being pushed to your device.

Internal Storage

This is a great question. The way the Nexus 7 and other devices that don't have an actual physical sdcard slot handle this is the sdcard folder you see in the file explorer acts as an emulated sdcard. So this way when you go to install a custom ROM in recovery mode when the ROM installation requires you to wipe everything the contents of the emulated sdcard will be untouched and remain as if it were a actual physical sdcard.

General

Busybox

Busybox is a series of stripped down GNU utilities and command line applets, you can find more about Busybox and what it is here. As far as needing it in the beginning you might not need it but as you get more familiar with modifying devices is comes in very handy for performing certain operations and tasks and is worth installing just to have for it's functionality. A lot of root programs push the su binary, a Superuser.apk, and often times the busybox binary. Not all ROM's choose to include busybox but it's handy to have like I mentioned for it's functionality.

Cyanogenmod

Cyanogenmod is an aftermarket firmware distribution you can find more about it here. As for why is it famous it was one of the first well know custom ROM's and soon grew to include support for a vast amount of devices you can find more about the history of Cyanogenmod here. AOKP is another well know ROM that stands for Android Open Kang Project, it first came about when Android 4.0 Ice Cream Sandwich was released you can learn more about AOKP here.

SuperUser

If your current ROM is missing a Superuser app you may install one from the Play Store, it does not matter which one you choose it is personnel preference but I would use either Chainfire's SuperSU app or Koush's Superuser app. Updating a pre-installed Superuser app to the latest Play Store version is fine. There are no consequences to installing one Superuser app and uninstalling another one it's a matter of personnel preference which one you want to use. Keep in mind if you uninstall one Superuser app and then install a different one it may ask you to update the su binary (Which it should ask you if you want to do that once you launch the app for the first time) before it will function properly.

If you have any other questions let me know I'll be happy to answer them or elaborate on anything that may still be unclear to you.