Which feat might that be? I cannot find such a feat in the PHB.
While that's true, it is often true for PCs as well. Our group took out a group of foes in HotDQ, then waited for more foes to show up. Plenty of time to get in a short rest, in fact, it ended up that the other foes did not show up until the next day because they had not yet been alarmed (they were a few miles away). This happen again the next day (course, we were outnumbered 2 to 1 with higher level foes that third fight).
Granted, there are scenarios where short rests do not often occur, but smart players often figure out ways to gain short rests.
Often the DM does not control the short rests. The players do. The DM controls the consequences of taking a short rest.
Unless players want to suck up a lot of their Potions of Healing and use a lot of their healing spells, a certain number of short rests are even mandatory to continue on. Someone in a group will be seriously hurt after many encounters.
Yes, if you are being defensive, you cannot be offensive.
This is no different than a lot of additional effects that use bonus actions. You can only use one of them.
You mean like 5E Wizards?
This is a fairly standard game element for D&D.
Shield Mastery: not particularly useful to monks, but awesome for fighters, monks, etc.
K is a very limited resource, that's the difference. Compare to the rogue.
1e, 2e and early 3e wizards absolutely. Late 3e and now 5e wizards? Not anymore, good cantrips, rituals and long lasting spells keep the wizard going even at low levels. WoTC clearly made a concerted effort to mitigate abs lessen wizard's early weakness!
You could steal from the World of Warcraft monk: Normal attacks generate Ki, which can subsequently be channelled for additional effects. Your level-based Ki limit is the maximum amount you can have stacked up at one time.
That was actually my exact thought.
I'm planning on giving the monk a "headband of ultimate focus." It will have charges like a wand and replenish like a wand. If it proves too much the charges will fade. If it proves perfect, the ki will eventually become inherent (it was him all along, bit cheesy, but hey).

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.