In popular non-game software (such as web browsers and operating systems), left-click and right-click work as I mentioned. Left-click is the default action, and right-click opens a context menu.
Same in Battle for Wesnoth (which has only a map, no inventory): left-click to move and attack, right-click for context menu. Most of the options from context menu except one are useful only in rare special circumstances. I think you intend to avoid having extra options, so there is no need for a context menu. That's good (well, it has its upsides and downsides, actually).
I have checked Diablo II and Dungeons of Dredmor, and on one hand you are right, but on the other hand, there are important differences which make Epilogue confusing for me, while these games are not. Left-clicking an item initiates a movement. This movement can be used to equip stuff. Right clicking is only for using consumables (which is done rarely), so I left-click most of the time. I try to do the same in Epilogue, to equip another item, but it works differently: the item is dropped. I have to fix the mistake: move the mouse, left-click to pick it up (and it will usually appear not in the same place as it was before the whole process), move again, right-click to use.
I see that your one-click-drop interface is faster for experienced players, but it is annoying and confusing for me.
Also, in all three games mentioned above, left-clicking on the map does movement, attacking, and other usual things (talking to NPCs, opening doors, whatever). Is there a reason why you cannot have left-click on map do the usual thing in most cases?
They also pop up exactly when you need them, which is much better than waiting until you think you need them. I.E. a fatigue popup occurs when you get tired, and the healing popup occurs when you get to the point where you can heal.
No, they do not. I have found a campsite, clicked on it, and it disappeared. Some time later, the popup explaining fatigue occured. Apparently I have wasted a campsite... The healing popup would usually occur in the middle of a battle (at least it did when I tried). I would prefer to finish the battle first, rather than read about healing. Theoretically I can close it, but I would not, because I expect it to be important.