1. Din's religion is a little bit silly, but the thing is, the Children of the Watch literally saved his life and raised him into the man he is today. He's absolutely and utterly sincere about his beliefs and he isn't giving them up at the drop of a plot convenience. That's something I think deserves a lot of respect. Bo-Katan doesn't believe in the "silly religion"; she's also literally a useless, depressed lump of sitting around basking in her self-loathing.
(Perhaps she, Obi-Wan, and Yoda should start a club.)
2. Lightsabers are harder to use than it looks due to the massless blade, and the Darksaber is said to be *especially* tricky, doubly so for a non-Force user.
3. Yeah, she can stop being a depressed lump of useless when there's an actual mission on the table. She *does* care, it's just...without a specific goal, all she had to do was wallow in her failure.
4. Like she told Grogu, "Did you think your dad was the only Mandalorian?" She's very, VERY experienced and has top-of-the-line Mando gear.
5. Remember that Bo-Katan had it or the entire period of time between when she was given it in Rebels and when the Empire blew everything to hell. She's had a lot more time and opportunity to practice with it than Din has, *plus* more motive to actually do so, on top of being overall a much more experienced warrior than he is.
6. Bo was reading the plaque out loud while she was semi-sarcastically giving him the "grand tour", while Din was staring at the Living Waters. It's not that he couldn't read Mando'a, it's that he wasn't looking.
7. Because he was too busy having a sincere moment of awe to think through what he was doing, and he had NO idea the stairs dropped off so suddenly. (For that matter, Bo-Katan didn't seem to anticipate that being a thing, implying that the abrupt cut was due to collapse rather than it was always that way.)
And while your point about heroism doesn't necessarily make for good leadership, Bo-Katan has also made her own foolish decisions in plenty, including some that pretty much directly led to the most recent round of genocide against the Mandalorian people, and that's on top of her family's entire legitimacy as 'rulers of Mandalore' being extremely questionable in the first place.
House Kryze and the New Mandalorians were literally the puppet government put in place by the Republic specifically to finish the job of genocide that was kicked off by what even the Jedi euphemistically call 'the Excision'. The NMs were even the ones who set up the Jedi at Galidraan to murder off the True Mandalorians specifically because the TMs were starting to form a legitimate opposition, and at several points cooperated with Death Watch for the exact same reason.