Is there a PDA for every Type 3 Grammar?
You need to check the definitions: type-3 (regular) is a (proper) subset of type-2 (context-free). Therewith, every type-3 language has a PDA that accepts it.

Essentially, you take a finite automaton for your type-3 language, add the stack but never use it. Up to minor definitory differences (e.g. w.r.t. acceptance), this gives you a PDA for the language. This is also one way to prove that all regular languages are context-free!