I have a conventional concave cornice and I get plenty of cobwebs in the 10mm step out from the wall plaster (but not so much the step out from the ceiling plaster, or maybe it doesn't show so much there). If you are replacing the ceiling I would go with a shadowline rather than square-set which will show every wobble in your plaster or paint. I don't think it is feasible to install a shadowline into an existing ceiling (which will usually have a ragged edge under the existing cornice) but I could be wrong...

Will look much better white BUT! Having done this to big old sliding doors and window frames in an apartment with more ‘steps’ in the frames there are a couple of things to watch out for. Sealing - as mentioned in another post is essential, if the wood is stained then the colour will come thru to the paint. I did this just as the manufacturers were getting the water based enamels right and have done several recoats since. Agree that Zinsser are great paints, I have used their wall and ceiling paints everywhere, cost more, are a bit more ‘drippy’ but also have a sealer component and actually do a real white that doesn’t yellow. They also last really well on the wall. When you transform to white - especially if you are thinking high gloss EVERY defect in the wood surface will show up. This adds to the charm or is a problem, depends on your perspective. I dropped back to a satin finish on wood trims. There is only so much prep you can do, sometimes it is easier to fix the obvious dings and then do another round after the first coat of white, after the sealer. This is harder to explain - but you can end up with a dark line around each window pane - because the glass is sandwiched between two pieces of dark coloured wood and the ‘inside’ of the wood shows through the glass and you notice it from across the room. I painted slightly onto the glass, a few millimetres to achieve a fully white effect. You only notice it if you look closely. Fly screens - wooden fly screens have the same ‘edge effect’ metal flyscreens are a bit easier to paint. They all look significantly better in white than the dark wood - in my case the two sets of sliding doors have very wide frames. Depending on your skills and patience you may want to get a professional. I am about to replace the south facing repainted bathroom and study windows with double glazed UPVC tilt and turn with white frames - no more arctic bathroom, jammed winder, condensation or mould. These are now made (licensed) in Australia so only have to pay for shipping from Vic to ACT rather than from ‘overseas’.

you may like to consider powder coated steel coving for skirting boards in your bathroom...should be available at any tile store and colour choice is very personal but same colour as floor can look more spacious

If you do it stop it at vanity height. However, I’d do all horizontal plank tiles to match vanity planks and keep it simple to let the lovely vanity shine.