These are good questions! I'll do my best to answer, though someone more plugged into the program would have better responses.
1) Hopefully the Scanlan situation is in the rearview mirror. I have to think, Gait would be the last coach on earth that would offer him any sort of second chance, seeing that he was the women's coach last year. The takeaways? It sounds like Scanlan had a number of previous unreported issues that should have been addressed (rumors of at least two fights with teammates). Have to nip things like this in the bud early on.
2) Syracuse definitely had some bad moments last year where frustration got the best of them. I'm not a coach, but I imagine taking guys out of games or some sort of discipline if they can't keep their emotions in check would help.
3) "Culture" is such a difficult thing to measure. To me it's a chicken or the egg type thing - are you winning because you have a good culture, or do you have a good culture because you are winning? I know a lot was made of UVA not bringing in a lot of transfers last year and that was because of their "culture". Duke fell apart and it was thought it was because they brought in too many transfers. So I think Syracuse has to be careful about who they bring in, but should still bring in impact players if they can. Also, it seems like a team would just be much more easy to manage if the numbers are lower. It sounds like long term this is something Gait wants to work on, but I don't know if he will make massive cuts to the roster. I might remember this wrong, but I beleive when Tiffany came on at UVA, he made a number of cuts to the roster that surprised people. It seemed harsh at the time, but perhaps Gait should do the same. Did Syracuse have culture problems last year? The covid protocal suspensions were not a good look to start the year, and raises some questions about how committed the team was, but at the same time, as a team they stood up to a star player and made a stand - not too many teams can say that.
4) It does sound like all three coaches will be heavily involved in recruiting which is great. I think its well known Desko didn't love the grind of recruiting, and I don't think Donahue was well known for recruiting either - that left most of it up to Rogers. Now you have March who proved himself last year, along with two of the biggest names in lacrosse history. Petro has proven himself a really good recruiter, and can draw from all over the country. Not sure what exact responsibilities get doled out to who but it looks like Gait was at the Long Island High School Championships this week while Petro was down in Maryland at an event. I'm guessing there will be a lot of dividing and conquering.
5) Faceoffs are tricky - Phaup had his struggles last year, but still had a 57% winning percentage, and like you said dominated LaSalla. I don't think you can just give up on him, but you need to have a more reliable backup. And in terms of coaching it felt pretty telling that he felt the need to drive down to New Jersey to meet with Jerry Ragonese when he was struggling. Someone on here mentioned that TD Irelan might be brought in as a voluntary coach, but I have no idea how true that is. If it is true I have to think that would help immensely. I don't think many teams have a coach who is considered an expert on face-offs.
I thought I would add my own question.
6) How does Gait make this team his own? I sincerely beleive it is great that Desko still plans on being close to the program, and that he's already had extensive contact with Gait and Petro. And Gait being an alum, and having previously coached the women's team helps with continuity, which again is certainly a good thing - but this program needed a shakeup. How does Gait establish himself and make it clear that someone new is leading the team.