Well, it's not a very strong computer, and it doesn't know what the most common continuation is. To its evaluation function, 6.Bd2 is better than 6.Bxe7, but the difference is probably tiny.
Same for 10...Qe7 - it think it's marginally better than 10...0-0 (-5.4 vs -5.1). Now a 0.3 pawn difference is quite a lot, if you're looking at differences between 0.0 and 0.3, say. But to us, a difference between -5.4 and -5.1 doesn't matter anymore -- winning is winning. But to the computer, it's the same difference.
About 11...Re8+: "why allow something like Ne5" isn't an argument to a computer; it is looking at concrete lines. If it sees a defence against Ne5 in all important lines after ...Re8, then it's not a problem -- regardless of the hassle and risk it would cause if you were to play it.
Computer analysis is good for pointing out tactics that were possible but missed by both sides. For the rest, this computer is too weak and should be taken with a grain of salt.
.. I guess you're putting a rook on an open file, which can't be bad can it? Then, instead of moving the queen to develop the bishop, fianchettoing him is an option.
.. but I guess the comp didn't seem too concerned about that (I can't be bothered looking at the threat on h7, late and I'm tired hah)
OK, so 6.Qh5?? was terrible, but how can 6.Bd2 be the best move? 6.Bxe7 is a trade of bad for good bishop, and it's the most common continuation as far as I know.
Moving on - How can 10...O-O be a mistake? There's no way to stay 2 pieces ahead for very long. Even the computer alternative 10...Qe7 eventually gives up the knight (and castles anyway!).
I agree with its suggestion 9...g6. That really does threaten to stay 2 pieces up.
I disagree with the suggestion 11...Re8+. Why take the rook off the f-pawn and allow something like Ne5, hitting f7 with the queen and knight? On that move, I thought I might want to keep the flexibility to put my rooks on f8 and e8, so I was in no hurry to play Re8+. Also, I figured I need to get my light square bishop out and therefore need to move my queen. I didn't want to just trade the queens. With an extra piece why not try to attack? So 11...Qe7+ looks just fine.
The most surprising thing about this analysis feature is how marginally useful it is. If I followed all the computer's suggestions I would find myself in the middle of a game I don't understand at all because the moves did not flow from any sort of logic or positional ideas. Maybe that's to be expected from auto-analysis, but it's clear that this feature is generally not worth paying extra for.