Is it possible to redo a quest?
Make another character
If you abandoned the quest, then yes there is an abandoned quest tab were you can redo it. If not then you can’t.
There are repeteable quest in some maps (green quest flag), mostly hidden so speak with every npc in the map to do all the quests.
If i made another character, can i transfer an untradeable item to my other character?
In cbt2 people found a way by editing some game files to allow taking same quest over and over again. Not sure if imc made quest completely server sided now, if not then you prob can repeat them none stop.
You can’t trade untradable item, but you can trade recipe of untradable items.
Really?! Do you know how to do it?! 
apparently even the recipe is untradeable… The rokas leather armor recipe