Black screen = missing or out dated IOS file
1. Some new games need updated IOS files. When you say "new firmware" you probably mean new/updated System Menu (3.1, 3.2, 4.1....). You don't need to update your System Menu, only IOS files. To 3.2U will not solve your problem, but to 4.2.
2. Yes. Check this guide: http://www.wiihacks.com/wii-modchip/...-hardmods.html
If you want to softmod your Wii you can follow this guide: http://www.wiihacks.com/recommended-...d-any-wii.html