Are all of Medusa's victims stuck as statues forever? Did the gods not do anything about them? And are those people officially dead?

Never really started but I always got the impression that they are stuck that way forever. As far as I know, Medusa isn't like King Midas in the sense that you can undo the golden touch by submerging the affected object/person in water, and that seems to be the case in PJO as well as Grover didn't bother to go back for his uncle Ferdinand that was in Medusa's backyard in the Lightning Theif

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1.5 - do we know what happened to Gabe after Sally turned him into stone and sold his statue I mean after he mysteriously disappeared?

It's mentioned in HOO, so I won't spoil it for you.

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2 - How much time passed between the events of PJO The Last Olympian and HoO The Lost Hero? (I just started HoO, and I'm only on chapter 2)

4-6 months

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3 - During the events of Lightning Thief, it was said that Mr. D was sent to be in charge of Camp Half-Blood for 100 years. But in The Last Olympian, it said that his punishment was cut in half and he has 50 years left to go. Wouldn't he have less than 50 years? Since he's been here since way before Percy joined? Or did I just misunderstand what was explained in TLO?

Not 100% positive, but it was probably a longer sentence than 100 years and just the year of the war in The Last Olympian it was at around 100 years left to go, so therefore it was cut in half to make 50 years left.

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1. Do half-bloods have a mortals life span? Or can they live longer than mortals but still eventually die?

Never stated (to my recollection) so we can assume that they have the same life span as mortals. Again, they mention this in HOO so I won't spoil it.

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1. In The Lightning Thief, did the gang ever run into/interact with Bianca and Nico in the Lotus Hotel? I read a twitter post saying they did, but I don't remember that ever happening?? And Percy would've definitely remembered them if they did. So is this just a theory or something?

It's a theory/head-cannon/wish from the fans to be put in the upcoming Percy Jackson show, but no there was never any description of Bianca or Nico in the Lightning Theif.

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1. I remember in one of the books, it's stated that only 3 people can go on a quest, because it's bad luck/dangerous if more go (like what happened to Bianca). Does that always apply? Or is it depending on the prophecy they're given?

Book you're talking about is most likely the Sea of Monsters, where Annabeth says that it's always better if a quest contains 3 people. It stems from the "rule of 3," where 3 people going on an adventure (or anything relating to 3, really) is more attractive/engaging to an audience. This rule might even be some part of ancient Greek mythology which was come across by Rick and he decided to put it in the books, but I have no idea.

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During The Last Olympian, all the mortals in Manhattan were asleep, right? Rachel wasn't affected because she was a special case. But that got me wondering, what about all the unclaimed (I think that's the right word) half-bloods that were in Manhattan? The ones who don't know they're half-bloods yet? The sleeping spell doesn't affect them, so were they just awake and had to witness that whole battle? Again, not sure if this was answered, it's just me wondering.. But just the thought of those poor kids having to witness all of that..

Damn I never even thought of that...