Like most Magic: The Gathering cards, the value of Hildibrand Manderville // Gentleman's Rise depends on a few consistent factors: its rarity, the printing and finish (regular or foil), its physical condition, and the set it was printed in (Final Fantasy Commander)
Giving permanents to other players can often bite you in the bum, but with Iroh's ability you'll benefit regardless of whether your opponents hand your stuff back to you or keep trading it back and forth between themselves like jerks
Like most popular XY-era Megas, it has trended up over the long run as the set ages out of print and Rayquaza demand holds steady
The print runs are once again not known but I suspect they are in the 5-10k range
(3) If this card is sent to the GY as Link Material: You can add 1 A.I. Trap from your Deck to your hand
Casting creatures while it's on the battlefield can yield a wide range of effects depending on what you need