It is certain that not every fixed point-free action is free. I saw in an earlier post (https://mathoverflow.net/questions/77715/s1-action-in-three-dimensions) in MO regarding non-trivial $ S^1$-actions on $3$-manifolds. I look at the paper "Actions of $SO(2)$ on $3$-manifolds" by Orlik and Raymond where they classify $3$-manifolds that have fixed point free or without fixed point free $S^1$-action. My question is as follows.
Question 1: Does every Seifert fibered $ 3$-manifolds admit a free $S^1$-action?
Question 2: Which Seifert fibered $3$-manifolds admit free $S^1$-action?
There were some comments mentioning that every such manifold will have free $S^1$-actions. I will be really grateful for any suggestions or references.