I agree with most of the responses, so I won't repeat.

3-5 coats is fine. light sanding to break the gloss and take off high spots with 220 dry grit is fine. actually you don't want to go too fine with the sanding grit here, because the sanding roughs up the surface to create a better mechanical bond for the next coat. the next coat of varnish will fill the scratch marks, so going finer than 220 is not helpful.

as the can of varnish is open to the air, it will thicken, so after several coats you will need to add more thinner to compensate - i've always found that "too thin" is better than "too thick".

the trick of heating the varnish in warm water works great - it flows and spreads much better warm - but the warmth accelerates the thickening of unused portion left in the can - so again, add thinner to compensate

spraying for this work is not worth the effort. a good brush job looks really good, and the spraying is very tricky to get right, plus the potential for stirring up junk/dust in the air is quite high.