Usually if its a positive thing you would say благодаря вам/тому (thanks to you/ that) and if it is a negative thing you would say из-за тебя (because of you). Ex: Благодаря тебе я умею готовить. (thanks to you I know how to cook) or из-за его болезни он умерю (because of his disease he died.)
You can say "из-за болезни он не смог пойти на концерт" (because he was ill he couldn't go to the concert), but when someone dies, we say "он умер ОТ болезни (от рака, от туберкулеза etc.)", not "из-за болезни". And, unlike English, in Russian we never use possesive adjectives before words like болезнь unless we want to emphasize it's that particular person's disease rather than someone else's disease. Otherwise, you are absolutely right.
It's not. In this case "благодаря" is a preposition. If it was a participle "благодаря [кого?/что?]", it would be followed by the Genitive case, because the verb "благодарить" requires Genitive, but here we have the Dative [кому?/чему?]. Consider "Благодаря + [noun in the Dative case]" an idiomatic structure.
This is, in fact, the only way, to say “thanks to” in Russian. However, it is important to distinguish between the preposition «благодаря» which is always followed by a noun or pronoun in the dative case (e.g. благодаря вам) and the adverbial participal «благодаря» which is followed by a noun/pronoun in the accusative case («благодаря вас» = “while thanking you”). The latter is hardly ever used, though, as the perfective counterpart «поблагодарив» turns out to be more appropriate in most situations.