Didn't know how well to word it, but how do you make another wolf become alpha? One of my females became Alpha Female, even though the older one is still alive, and I want to breed her with another male to make them the new alpha's. How do I do this? Is there a certain skill they need to have higher?

If you increase the other wolf's Dominance past the current alpha, they will become an alpha.

I've seen some packs where one of the alphas have lower dominance than even some omegas, same goes for betas, how does this happen?

They're most likely the other gender.

But the beta female beat out the old female alpha, and they both had the same Dominance points, so that doesn't make sense. Or is it only females that do that, and the only way for a new alpha male is if the old one dies?

If you have the same Dominance points, they will fight over the position. If you want a specific wolf to be a certain rank, change the amount of Dominance they have.

And if they have the same amount?

Please re-read the above:

I had a pup called Tiger whose dominance is 1. I also had an alfa called Griffin whose dominance is 1. The pup took over when he grew up...

they have same dominance. add more to the former alpha if you want him back as alpha