And plastic for the Plastic Throne!
No! This is not a board game, but Stanislao Moulinsky in one of his best disguises!
1.can you move titans with the card pegasus??I think that you can't move
I think you can: in the Titans rulebook there's a note for using the Harpy against a Titan (which you can't do) but none about using Pegasus with them.
So, since both creatures are from the base game and no objection is made about Pegasus, I infer you can: and you don't even have to pay for the movement, as long as you move troops and Titan(s) from a single region.
2.lets say that the first player play the card GRIFFON and he steal the half coins from the second player.After this move on second player's turn he can't pay the favor to the god (because the griffon) what is happening in this situation?
All the offerings to the gods happen at the same time, as soon as the bidding phase is over: thus, in your example, the second player has already paid his due to the god and the Griffon only steals half of whatever the second player still has left.
3. In a 3 players game we've got 5 gods tiles.We shuffle them and
a)We open the 2 tiles of them
b)Then we open from the 3 closed
c)we open the last god tile and we shuffle the other 4tiles and open one?
When playing with three players, the Titans rulebook states: "The last three gods are placed face down. Two of them will be randomly placed in the first two spaces during the next cycle".