So let's say I were to throw {Dragonshift} on a {Young Pyromancer}. Would I get another token if that's the only Pyro on my board?
Yes because the pyromancer triggers resolves before dragonshift does
Yes you would get the token. Here's how it works:
1- you cast {Dragonshift}
2- by casting an instant or sorcery, you fulfilled {Young Pyromancer} requirements for his triggered ability. His ability goes on the stack above {Dragonshift}.
3- if your opponent has no response, you get a 1/1 elemental
4- {Dragonshift} resolves. If overloaded, all creatures you control (including your new token) become 4/4 flying dragons.