Are there any areas and/or monsters that have a better chance of dropping gems and what is the highest possible gem quality that can be dropped? How can I maximize my gem farming procedures?
In my opinion, the best place to farm gems quickly is act 1 inferno. In act 1 inferno, flawless squared gems are dropped, and those are the highest gems that can be dropped.
If you'd go to act 4 inferno, the same quality of gems would drop, but the pace at which you could kill enemies would very likely be much slower. Stay in act 1 because monsters are relatively easy there.
Obviously, keep your eyes open for resplendent chests and treasure goblins, but that goes without saying.
The best way to minimize the time needed to get higher quality gems (which is ultimately what you will go for - even if you want to farm low-level gems) is to go to higher difficulties as fast as possible, since stronger enemies will have a higher chance of dropping higher-level gems.
This does, of course, mean that special opponents such as champions, bosses, or the treasure goblin have a higher chance of dropping them, but unfortunately, I don't think there is a place with tons of champions always walking around. Basically, you're up to your fortune here in how lucky you are to find gems.
The thing with gems is that there are a lot of different quality levels with them this time around. As far as I'm aware, there are 17 of them. If you spend a noticeable amount of time in one area just to grind for gems, you're most likely just wasting you're time, because the same time spent on advancing in the game will get you more higher quality gems earlier on. e.g. at the beginning of nightmare difficulty, monsters still drop mostly flawless or normal gems. At the beginning of Act II already, they're dropping mostly perfect gems and if you're lucky, radiant gems. This means that farming for gems is mostly a waste of time.
An update, as much of this info is currently outdated.
It seems that running the bounties that kill bosses (any diablo-head icon next to the waypoint on maps with the associated bounty, such as Belial, Magda, etc) is the quickest and most profitable way to farm gems solo.
I have finished my third boss and have 20 marquise and 3 imperial. Note: this is solo with 0% MF at t16. You're always going to get better drops at more difficult levels.
I find that just encountering elites and whatnot do not guarantee gems, and I prefer not to bother with [g]rifts for normal gems.
I've found that the best places to farm for gems are inferno any act. The max gem is flawless square and that is also the min gem. These are the only gems that drop. But here is my experience on getting more... purchase 2 puzzle rings from the auction house, then equip you and your follower with one each. A goblin will spawn every 10 - 15 minutes in addition to the goblins already there, greatly increasing your chances for gems. It'll set you back a few million for the rings, but for the addition, I reckon it's worth it.
He stated that because obviously it is the highest difficulty, last act. Therefore better monster/better treasure scenario.
I find the best way to farm gems is to simply play lots of public games, join one, kill boss, leave and join another random game. I feel that yes even though you are grinding, you are skipping most of the fodder and advancing straight to elites/bosses and so forth.
I currently am lvl 40 monk on nightmare difficulty, and I am finding tons of gems in Act II. The monsters here are easy enough to kill yet have a nice drop rate it seems for random gems.
Currently I am wondering if %magic find helps since gems are whites.