Is it possible to teleport the player to a new location using dialogue? For example, if the player asks an NPC for a ride on his cart and then teleports to the destination?
Yes, it's possible and pretty simple:
In the Dialogue selection you want to have initiate the teleport (in the keyword editor), go to the ACTIONS box and type in:
ACTION SetFlag("FlagName",1)
Then
In the story editor, make a new script and in the KB section
IF
GlobalEventSet("FlagName")
THEN
CharacterTeleportPartyToTrigger(CHARACTER_Player1, TRIGGER_DesinationName,""_)
That should get you going.