From what I've seen, my friend, people here are typically against doing others' homework. You obviously just made an account today with that in mind.
I'll help you with one part of your question:
j? is complex frequency, though actually technically that's just the imaginary part. The whole term is (?+j?) where ? (sigma) is the real part and ? is the imaginary part. When you learn Laplace transforms in the context of electronics, which I doubt you're doing right now, you find out that s, the complex variable used in the transform, is ?+j?. When you just pay attention to frequency, such as for the Fourier transform, you only analyze using j?. This is a big one for students: When some teachers may write a transfer function, they may write G(j?) or just G(?) and they may even use them interchangeably in the same lecture. They mean the same thing and it's just preference, really. G(j?) is technically the most correct, but engineers don't seem to go out of their way to make mathematicians happy. G(s) is something different entirely and is basically the same as saying G(?+j?). The ? in (?+j?) allows you to capture amplitude effects as well as frequency. You can model both decay and growth of the amplitude, which is important in real-life situations. Working with frequency only assumes that the signals go on forever unchanged, which, given that the universe will eventually experience heat death eventually, is impossible.
EDIT: WTF? What kind of EE-related forum doesn't use proper unicode? The lowercase omega is just '?'...