It may be that Comey's handling of the email investigation during the election was egregious enough to can him, but the circumstances and timing are bizarre.
Reasonable normie: It is horrid PR. Trump (or his advisers) must know how bad it looks to fire someone who is investigating you and even worse when a pattern emerges. Could they really be that naive to think they can control the narrative on this story?
Paranoid conspiracist: It is a way to fan into flame the slow burning Russia story to distract from something else (healthcare, nepotism, budget, lies ...) Are they that clever? Is it a necessary step towards appointing a stooge?
The simpler explanation is that Trump's administration is inept or misinformed but those are worrying conclusions.
I'm reminded of the incident, when it was beginning to come out about the Benghazi scandal with Hillary, where Bill Clinton and Attorney General Loretta Lynch privately meeting on a landed airplane and it being caught on camera. The story that Loretta stuck to (I can't recall Bill's side of it, likely the same, he's too savvy to fall into an obvious trap, I think) was that they happened to meet accidentally and they mostly talked about their families and grandchildren in particular. Of course, no one who was convinced Hillary had done some wrong with Benghazi bought that for even half a second; how likely is it that you "happen" to meet someone on an airplane tarmac, in a private jet, and then fail to fly anywhere after?
Given the circumstances, it could only possibly look bad. Given that Loretta and the Justice Department later did nothing regarding all this, I bet neutral people found it massively suspicious as well. It's another case of timing and circumstances being bizarre. The most conspiracy-theorist side of me also rates the numerous mysterious deaths surrounding the DNC in the lead-up to the election as incredibly suspicious too.
I think lots of people in positions of power and influence think they could control the story; all too often people like this get surrounded by yes-men, and they're all inside this "bubble", so to speak, so they don't have people who are more grounded in reality with the courage to say "you're a fucking dumb-ass, this shit isn't going to fly", and so they find themselves in these bad situations.
No and somewhat.
I don't think Trump and his team are stupid, although I don't rate them as particularly smart, either. But lots of presidents do things like this, throwing consequences to the wind because, ultimately, who's gonna stop them? The only ones with the power to impeach or stop actions he takes are Congress. Republicans control both houses, and unless things get completely out-of-control, not one person from the Republican Party is going to say "let's impeach our own president and put a stain on our party that will never go away."
As for the stooge, well, all appointed positions are stooges to some extent. You appoint someone because they basically will do what you say. Positions like Director of the CIA, Head of the Department of Justice - these are political positions, whether they should be or not. You get there because you have 2 things: political clout, and the trust of the President and his staff that you'll do right by them and advance their policies. If you don't have those things, you don't get the job; you're not even asked for a resume.
I don't think I've seen a truly competent administration, at all or even most levels, in my lifetime. Not sure why this one would be any different.
EDIT: Had an incident wrong and changed a couple sentences to correct it.