The next set of questions I suggest asking at a messianic congregation is:
What led you to become part of the messianic movement? Who teaches you or where have you learned from? (Then research those teachers.)
Finding out about the origins of a person’s belief system is always helpful, but the testimony of a leader can be especially important. It may not cause you to decide to go to a congregation or not to go, but it can at the least help you understand where the leader is based.
They may have entered the movement because they are Jewish, or because they became convinced that God’s Law is for all Christians, or at least that it still has some kind of application today beyond what is typically taught in Protestant churches. They may have entered the movement in a state of rebellion against traditional Christian theology. This isn’t always bad, but combining it with another question I’ve suggested as to how they regard nonmessianic believers can reveal a lot about the leader’s state of soul.
Entering the messianic movement for the wrong reasons or with the wrong spirit usually means a leader won’t be taking his congregation very far beyond the point of rebellion. They will exist in order to be different than the rest of the Body of Christ, not to serve the Messiah or His Kingdom. Or, at least, they won’t be able to do it well.
The next question is perhaps an obvious one, but not one that we always think to ask. Since most messianic teachers haven’t gone through seminary or been approved by a denomination, the tendency will be for them to be mostly self-taught or have sat mainly under one teacher, or to be mostly influenced by one teacher. That can be deadly in the messianic movement, which has some real whackos running around as teachers. So ask the leader where they have learned about the faith or where they are learning from currently. Then, investigate that source of teaching yourself. Be sensitive to any red flags that pop up while you’re researching. Run teachings that seem to be a bit off to you past trusted friends in the faith.
If they say they’re self-taught, ask what books they’ve learned from and then get copies for yourself.