Can Adobe Audition Separate the Sound Effects from Music(, like with these Audio Clips that are attached to this Post)? If it can then how do I go about doing it? However, if it can't, then what programs can do the job of Separating the Sound Effects from Music?
No software at all will make a good job of separating sounds like that, and Audition doesn't even begin to. It's a bit like baking a cake; once it's baked, you can't unbake it back to it original ingredients. There are a couple of bits of software that claim to be able to do something like it (try Spleeter, for instance) but I've never heard anything that could even remotely be called 'usuable' coming out of them.