Some questions
How the titans appeared?
Unknown, however people suspect they aren't a natural/wild phenomena, specifically this can be seen in how Commander Erwin reacted to the reveal that Eren was a shifter last season.
What's the relationship between normal titans and shifter titans?
Normal titans don't appear to have a limit on their regenerative abilities, they also don't display sentience. Shifters seem to have a limit until they are "worn out" as seen with the Annie fight in the forest last season, and Ymir defending the tower @ the outpost.
Are all titans just humans that couldn't transform back and eventually forgot they were once humans?
Unknown.
Who/what is the Beast titan? From where does it comes that he didn't know about 3d gear?
As far as we know, he's just another shifter.
What and where is the 'hometown' mentioned by Reiner?
In today's episode, it was implied that their supposed hometown is A) bullshit B) An alias for the place they are from.
Is there a place outside of wall full of sentient titans, like Reiner, Annie, etc?
We've been outside the wall early last season, before the fall of shinganshia (sp?). There were only regular titans outside.
Is that the village from where they came from?
Unknown.
Why that holy crusade of destroying humanity?
I'm not sure where the holy part is coming from, but Reiner hasn't elaborated on why he wanted to eradicate the humans within the walls.
Did humanity sinned greatly in the past and Titans haven't forgotten?
Not sure where this is coming from either.
Is Ymir from a different place, or from the same place than them but with a different goal?
During the flashback, the show states only Annie, Bertolt, and Reiner are from the "village"