You need to understand how the Wii's content is managed.
The Wii has "slots" where you can install system files to it (a slot is only a folder with a number, from 1 to 257).
each IOS that nintendo is making is installed in one of these slots.
For example IOS37 means that the slot (folder) numbered 37 contains an IOS (system file/program/functions) used by games to communicate with the console's hardware.
Each application or games you run on your Wii load one of the IOS (and only one) to be able to interact with wiimotes, USB, etc.
cIOS 249 means : custom IOS installed in slot 249
It doesn't tell which IOS content is installed, it only tells you that "slot 249 is used and it contains something".
it can contains anything, what you want to know is the content of that slot, or else it will have no useful information.
cIOS d2x : This is the content.
cIOS is a modified, patched, IOS, based on one of the IOS from Nintendo.
Each game requires specific functions, like access to USB (for microphone, or Wiispeak for example), and this function is only available in a specific IOS by nintendo (USB is in the IOS installed in slot 58).
What hackers are doing is : Take IOS 58 as base, modify that file to add more functions (like Reading games from USB instead of Disc).
The resulted/modified IOS is called cIOS (custom IOS, patched IOS, modified IOS, what you want) and it must be installed somewhere on your Wii for games to use that patched IOS instead of the original IOS.
Nintendo released only few IOS, installed in slot 1 to 80.
As there are 257 available slot, hackers started to install the patched IOS in slot near the end of the available space, and 249 was chosen randomly.
There are different patched IOS type used by USBLoaders:
Hermes, Waninkoko, d2x, (There's also on-the-fly temporary patch solution (patchmii, ahbprot) but I'm talking only about permanent installed solution for now).
They are patches created by different hackers.
d2x being the newest type (it's an update to waninkoko cIOS).
As the patched IOS had multiple releases, bug fixes, features (support for FAT32, support for Big HDD, etc.), there are multiple released versions of a same cIOS type. for example cIOS rev17, cIOS rev21, d2x v8, d2x v10
How to interpret this :
cIOS 249 D2x v10  : Slot 249 contains a patched IOS of type "d2x version 10" based on the original IOS installed in the slot 56. It contains all the functions the IOS 56 can do, plus an additional SD/USB access for USBLoaders.
Now about DIOS MIOS.
The Wii can play GameCube games by using a specific IOS used for GameCube emulation. (you see, what I explained above, each IOS has their own purpose)
That IOS is installed in the slot 257 (called the MIOS slot).
DIOS MIOS is a modified/created MIOS.
As your Wii has only one MIOS slot, when you install a MIOS, it replaced the current MIOS with the new one. to change the MIOS, just install another one and it will overwrite the previous one.
there are different MIOS :
MIOS : official from Nintendo, play official game disc
cMIOS : from wiigator, let you play backup from burned disc
DIOS MIOS Lite : From Crediar, let you play backup from SD card
DIOS MIOS : From Crediar, let you play backup from USB
To play GameCube games, you don't need cIOS 249 at all.
GameCube use the MIOS slot, not the slot249.
Slot249 may be used by some Wad Managers (homebrew to install content on the wii) to get access to the internal Wii's NAND and install DIOS MIOS in slot MIOS.
But it's not required as some manager don't even need a patched IOS to access the Wii's internal memory.
Some managers need to load a patched IOS to get access to Wii's NAND (the internal storage space), and some manager don't even need a patched IOS to get access to the wii's NAND.
Some managers which need the patched IOS can let you choose which slot to load in memory to get access to the Wii's NAND, and some managers auto-load the content in the slot 249 or 236 without asking you.
HBC -> Wad manager -> ask which patched IOS to use to get access to internal Wii memory or auto-load patched IOS in slot249 or don't load patched IOS -> get access to Wii's NAND -> Get access to SD card and USB to list wad files -> install wad's content in your Wii.
If it allows you to select a different IOS to use in order to get access to the Wii's NAND, you can select IOS236.
But I thought it would ask at the beginning, when loading the manager, not after selecting the file to install.
Most of the time, black and white screen means you are trying to play a game that is not from your region. The regions are NTSC-U = North America, NTSC-J = Japan, PAL=Europe, the regions may also be abbreviated like U, J, P. Look in the loader you are using and see if you can force a specific region, there may also be some other region settings in your loader. Last, some out of region games you will not be able to get working correctly, just give up and get a game for your region.
in order of best choices when you have this problem with any games:
- use component cable
- play a game from the same region of your Wii/TV
- try forcing video mode to match your game's region
- try forcing video mode to match your Wii's region
- try VidTV patch (with either of the above forced video mode)
- play more with video settings in loaders, try different combinations.
as you try to play gameCube games:
The main video mode is decided by the "DML Video mode" setting.
- if "Auto" doesn't work, try video mode "none".
- if "none" doesn't work, then you can try to use the loader to force a video mode instead of letting DIOS MIOS choose a mode automatically.
depending on the loader you are using:
Set the "DML Video mode" setting to anything with "force video mode"
Set the "DML Video mode" setting to "use one of the loader's mode" and choose one of the available video mode in the loader's setting.