How to farm exalted orbs?

What location, level, difficulty etc?

Any. Kill stuff. Lots of stuff. Hope you get lucky.

They can drop anywhere. No point in trying to farm them. Just farm other currency (or rather: items that you sell for shards) and convert to exalted orbs through trading. In 1550 hours of playing since the Steam release, I found two exalts. I found other stuff worth many dozens of exalts, however.

Davy jones locka

If you're trading, it's easier to farm alts and vendor-trade them up to fusings and trade fusings for exalts. But that's really a lot of work for that.

Most simply buy low/sell high to get rich.

In a trade-based game, "how to farm for X" is an ill-posed question. You don't farm for something specific, you get wealth in the best way you can and then buy what you need. It would be like asking in the real world "how do I get 50-dollar bills". Or, even better, "how do I get chicken nuggets".

I'm convinced that merciless Dominus has an implicit chance to drop them. Almost half of my exalt drops last season were from him.

Pure RNG. I have been farming Dominus for days back then and no exalt was dropped. This is what makes the game so fun and random, you can't farm anything specific in this game except for chaos/regal recipes with high MF but it is a lot of work indeed and it might take days to get just one exalt unless if you are farming 12+ hours a day. Also farming dom/piety might get extremely boring after some time but it depends on the person I guess. I like maps with high quantity +140% now that s real business.

If you focus your attention on any one activity, you'll come to think that that activity is the cause of your luck. For me, it's breaking pots in Catacombs. I've gotten 3 of my 9 exalts that way.

Play maps, which give you quantity bonus.