Ah, tablets. I just hope you won’t abandon keyboard support.
I expect some of your example actions were mainly for example’s sake, and not necessarily planned, but I’ll comment on them all anyway. 😉
Repair:
In-slot repair would be very welcome.
But the worst thing about repairing items is not so much having to drop and recollect them, which could be seen as a normal in-game hardship; it is having to deal with the inventory each way. I assume that work is ongoing to improve the Equipment/Inventory/Crafting interface so I haven’t made any comments about that, but what works best for actions will depend a lot on how this interface works.
Equip:
Again, the inventory+etc interface is the real issue. Drag & Drop wouldn’t be so bad if the equipment and inventory slots were not competing for visibility.
Still, an Equip shortcut would be better.
Quickslot:
The point of quickslots is that they are already set up for use most of the time, and not often changed.
Making this easier is not a high priority, and may instead make more important actions less convenient through added clutter.
Examine:
This is best served by Hover, as now, although I note possible refinements below. The main point being to keep it clear; less info-dump, more context-specific.
Dismantle:
Could be a cool addition to gameplay if one is forced to get creative in awkward situations.
Empty Water Bottle:
Assuming that you’ve accepted my idea about being able to (Right-Click) pour bottled water into open water (with no contamination), this might be useful if we find a pre-filled still or similar non-open source in the middle of the desert while carrying sea water. Otherwise ???