User blog comment:PsiCubed2/Question: General breakdown of levels up to Second Order Arithmetic/@comment-30118230-20180204192313/@comment-1605058-20180205123506

2. One such theory I have found is a somewhat technical variant of a reflection theorem, formalizable in second-order theorem: for any true \(\Pi^1_4\) formula \(\varphi\), there is a "\(\beta\)-model" in which \(\varphi\) is true. In second-order arithmetic, an \(\omega\)-model is some set \(X\), which we view as coding a countable set, which we further consider to be the set of "all subsets of natural numbers" for a model of second-order arithmetic, and then we can make sense out of whether second-order arithmetic formulas hold or not. A \(\beta\)-model is an \(\omega\)-model in precisely the true \(\Pi^1_1\) sentences hold.

All this is rather confusing, so don't worry about all the details - the point here is that this is some translation of the reflection principle which makes sense in Z2.

I'm afraid I can't give an answer to 1 nor 3 though.