I want to make a project involving many small dots indents and I would like to know how I can calculate the smallest dot hole the Prusa i3 MK3S can extrude around on a layer using PLA. In other words, if I printer a mesh with circle shaped holes, how would I know the minimum diameter of the holes. Is it simply the same as the layer resolution (0.35 mm), filament size (1.75 mm), or is it something else?
There is no direct limit on the size of a hole in XY-plane (that means: oriented so that the hole is visible from above).
The movement accuracy of MK3S (and most other modern 3D printers) is about 0.01 mm. So theoretically you could move around a circle that has diameter of the (default) 0.4 mm extrusion width + 0.01 mm, and get a 0.01 mm hole in the middle of the circle.
In practice, the hole size will be limited by the repeatability of the extrusion width. If in the above example the extrusion width happens to be 0.41 mm instead, there would be no hole remaining.
On a well calibrated printer, 1/4th of the nozzle size should be manageable, i.e. for MK3S you should be able to get 0.1 mm holes quite reliably.
That depends on the ability how fast you get filament to stick to the build plate and whether the filament is loaded in the extruder. It also matters which size of nozzle you are using. The filament diameter has no influence other than smaller filament width (e.g. 1.75 mm) requires more length to extrude with respect to thicker filament (e.g 2.85 or 3.0 mm), and is therefore more precise to lay down (on the other side is the deviation on the filament diameter, i.e. manufacturing tolerance, larger than for thicker filament...).
If it does not stick you need more length, also, if the filament is not preloaded enough, the nozzle chamber needs to be filled first. Note that the printing of several small circles is a challenge, see e.g. "How do I get circles on small interior holes to adhere to the bed?".
The only way to know exactly what limits your model, printer, slicer, and filament operate under, is to test it. While we can provide some guidelines, actual performance varies on a complex set of inter-connected variables. Even the room temp/humidity, filament age, and even filament color, can matter at the tightest margins. You have to consider what the print direction for the holes is (z/x/y), as layering matters even more than the above. And under what print speed and layer height? There's billions of combinations just with your printer alone.
Bottom line: run some test prints and see what you're satisfied with.
Let's look at how small we can print, shall we? Well, we have this filament, it gets pressed into the chamber, melts and then moves out a small orifice. So the first thing that limits print minimum is nozzle diameter, which correlates with the extrusion width - usually, I use a factor of 1.1 nozzles for the extrusion width.
Next factor is the bed or surface you're printing on which correlates with the Print material: some surfaces literally love to take your filament and allow your printer to extrude just a dot, then lift up like PLA onto a well-prepared surface. Others REALLY don't want to stick, demanding you to extrude more, which means you need to draw a circle (POM).
A lesser factor is the print temperature, which changes how vicious the filament is and how well you have dialed in your retraction, which determines how much of a "dead" move you have to have on the extruder to get the filament to extrude between dots.