1. What strengths / weaknesses does he have as a coach?
He empowers his players to take ownership of their performances. According to the
six styles of leadership by Harvard's Daniel Goleman he's a coaching type leader - he doesn't coerce people or micromanage (at least not that is obvious). Probably part of this is because of his youth and inexperience, he doesn't have the gravitas of a Carlisle or a Popovich to just come in and throw his weight around, another is because he's coming into a situation coaching a team that already has a solid core of leadership that has been together for years and made it to the Finals so he doesn't feel the need to make wholesale changes to style. I think he sees himself as more of a senpai, guiding them and keeping them focused on the goal. So that's why I think you see him spending a lot of energy on getting the players trained up in thinking for themselves, in reacting to situations because it's all about experiential learning. Sometimes this is to the detriment of daily results, because I feel he's willing to lose games as long as there's teachable moments in the losses. And obviously his biggest weakness is lack of experience - it's hard to be thrown into the cauldron and learn on the fly. I'm sure that like the players, he's also learning and there are things he would take back if he had the chance.
Of course, all this is based on what little I see - I don't know how he acts in training, or in non-game situations.
2. Can the weaknesses be covered up by hiring different assistant coaches?
I'm sure they can, and that's probably something they will look into at the end of the season. Brad and Wyc don't strike me as the type of people who overreact to things that happen during the season.
3. Did management make a mistake promoting Joe without a safety net? Should they have acted sooner to address coaching (i.e., when the Ime allegations came to light internally in June)?
I don't think so, obviously the Ime situation threw them for a curve, but most competent organizations always have succession plans in place, and their succession plan clearly included Joe in some form, otherwise they wouldn't have let Will Hardy go. So letting Joe and Will interview for the Jazz position but only letting one of them be recruited suggests that they considered one of the two as a viable candidate to succeed to head coach if anything happened.
4. When Tatum says publicly that he preferred Ime to Joe, what do we make of that?
I don't really make anything of it. Technically what he said was
Ime was his favorite coach, and I think that's ok. You can have a favorite boss and still be able to work well with your current one.
5. Where does he rank among NBA coaches currently?
Well if we go on the basis of results, his team is coming second in the East and has led the East for most of the season, so he must be doing ok

I would put him in the top 15 on that basis. I also don't know enough about their setup to know how much of that is due to Joe and how much is due to the players, but I do know that together they have achieved that result. But ultimately he will be judged on his ability to deliver a championship.
6. How important is coaching, particularly in the playoffs?
I think coaching is really important, but not for the reasons a lot of people think. I think just as you can have different types of leaders, you can have different types of coaching styles. For example on one end of the scale you have the NFL style coach where they exert a huge amount of influence in game, they tell the quarterback what plays to run or the defense what scheme to get into, they sub players in and out, it's like they are the person playing chess with the players as pieces. It works because it's a game with many stoppages and each stoppages allows the coach to exert influence on the game.
Then on the other end you have a soccer or rugby coach where, because of the nonstop nature of it once the game kicks off it's really up to the players on the pitch to organize the game, they have a number of set plays and patterns but because of the nature of it it's largely adlib and reactionary. The coach can yell instructions from the sideline, I doubt the players even hear him

At that point you have to trust them to execute what you did in training or practice and you trust you put the right players on the pitch to do that.
Basketball kind of falls in between those two extremes for me, you always run plays in practice to get specific players open, like a horns play to either get pick and rolls for your shooters or get the ball in to your post player, or a fist play where you screen the screener to get a perimeter shot, so I'm sure they know all these plays but it's left to the judgement of the players to decide which play to run. So other than ATO plays where the coach has the chance to draw up something specific (e.g. the Tatum three against Philly where he was in the backcourt and got himself free to take a pass from Smart at the perimeter going downhill, I think his influence in that respect is more limited than people think.
Unlike most folks here, I don't think his reluctance to call timeout move the needle more than his decisionmaking when it comes to putting players on the court, which is probably the biggest in game influence that he can have. And the second biggest influence he can have is to make sure he keeps them on track with what the overall tactics are, e.g. against Brooklyn where they devolved into isolation plays instead of doing what had gotten them to a 37-15 lead. In the playoffs, it becomes more pronounced because games are closer, and there's less scope for "letting them learn through experience". That's what the regular season is for, come playoff time you're trying to win every game. I would be disappointed if he continued his "hands off" approach come playoff time when the time for teaching moments should be past.
Where I see the coach having the biggest influence is in getting a team to buy into a style of play that will bring success, developing combinations that will be successful, and to maintain that over a course of a season, and to maintain a harmonious locker room regardless of who is getting minutes or not. And the results of that tend to show out over a period of time - over an entire season. E.g. if we had judged Ime before our run last season most of us would have wanted him fired. Right now Joe has the team in 2nd place in the East. How much of that is his doing vs the players is hard to parse, but together that's their body of work to date. They're wobbling a bit but there have been wobbles earlier in the season too. I think the challenge is to keep the wobbles short and to recover quicker. So far we haven't gone on long runs of consistently subpar play, even though some of the players have had peaks and troughs.
But ultimately Joe will have one metric that he will be judged on - whether he delivers a championship. In some ways its unfair for a first year guy to have such a high bar, but that's the reality of the position he is in. Everyone calling for his head will be singing his praises come season end just like they did with Ime - if he delivers a championship. If not then all bets are off
