How would, with the new weapon system getting added, level up. Would it be the same system, or different?
Would the behemoths be able to free roam, so you can use bait (like pursuits), and if so, would the behemoth be able to fight each other?
How would the new exotics work, and will there be new equipment like variants of armor for dires, lanterns, and Omnicells?
The current plan is that weapons will level independently in the new system. Each sword should be unique enough that leveling things as a 'class' of weapon no longer makes sense. Leveling will still be via experience, with crafting being involved to unlock perks and abilities on the weapons as they level up.
In a sense, this also addresses your question about new exotics. We are looking at moving to a place where each weapon in the game has the kind of uniqueness that an exotic does, making your weapon choices between any two swords, etc, quite important.
As for Behemoths, it is currently the plan that Behemoths will be less tethered to arenas, able to move around the islands more freely. Additionally, the new hunts we have planned are meant to find a middle ground between the old pursuits and the current Hunting grounds, and put you in a position such that you will know up front what behemoth you are targeting and can be assured will be on the hunt.