Is homebrew software illegal?
Making homebrew is most definitely not illegal. Actually distributing it or running it on hardware is a more sticky issue. All these devices have some form of protection system that necessitates circumvention to run unsigned code. Circumventing copy protection is usually illegal.
Is downloading homebrew illegal?
Yes it is illegal.
Is the Homebrew Channel safe?
Homebrew safety
There have been no known cases of the Homebrew Channel or BootMii directly causing any problems, and even if they did cause a brick, it should be fixable.