<ol>
<li><p>Is it possible to 3D print multiple 0.1 mm high layers with a 0.4 mm diameter nozzle in FDM while ensuring fidelity to the set layer height? The raster width is set at 0.4 mm and I am not touching that. The part thickness is 3 mm, so 30 layers of 0.1 mm have to be deposited for the completion of the print job. My polymer is PLA.</p>
</li>
<li><p>If not, should I be using a 0.2 mm diameter nozzle for this purpose?</p>
</li>
<li><p>Can a 0.4 mm print nozzle print rasters with higher width (0.5 mm, 0.6 mm, etc.)?</p>
</li>
</ol>

The
general consensus for nozzle diameter versus layer height
is to limit the layer thickness to eighty percent of the nozzle diameter. For a 0.4 mm nozzle, one usually limits the layer to 0.3 mm. The printer on which the nozzle is installed will determine the minimum layer thickness, often a typical value of 0.10 mm. I have printed successfully to 0.10 mm layer thickness with a 0.40 mm nozzle.
The linked site says just about the same as above, but also provides useful information regarding appearance, speed, strength, etc.
With a "next size up" nozzle of 0.6 mm, you'd want to limit the layer height to 0.48 mm but you might get away with 0.50 mm layers as there is some wiggle woom.
For 0.8 mm nozzle, you can get your 0.60 mm layers as the max for that nozzle is 0.64 mm.
The article also references that one can print wider than nozzle dimensions by increasing the extrusion factor, which may go by other terms, depending on the slicer used.