Mounting a boss requires you to leap from a ledge and perform an aerial attack on the monster - if it connects, then the mount minigame starts. However you cannot do it back to back. You can also use the aerial style which changes your evade animation to leap over monsters or the Kinsect Staff weapon which has a specific attack propelling you in the air.
As for weapons, i basically like them all. The change in playstyle is immense and basically when used correctly, every weapon is good (while some may be more effective against certain monsters). Dual swords are fast, but the they deal less damage per hit, have a faster sharpness drop and don't let you block attacks. Also they've the shortest range in game. Lance on the other side has a huge range and its defensive capabilities are insane.
It's all about getting used to the playstyle and be effective with the weapons. Everything is pretty balanced, in 4U they added the charge blade which was honestly over the top but they nerfed it on MHG.