Isn't friction from the atmosphere already slowing the planet's spin? Many weather effects like hurricanes ultimately derive their energy from a combination of the earth's rotation and thermal/uneven heating effects so I don't see why this is contentions.
Like most things, nature is already doing it and has been for millions of years.
Why would angular momentum be conserved? Rotation within an atmosphere should cause friction would should convert angular momentum into thermal loss.
Interestingly, it looks like the upper atmosphere generally rotates faster than the planet, so it could be that the opposite effect actually dominates. IE the uneven heating causes a atmospheric bulge that actually pushes the atmosphere around slightly faster than the planet rotates, thereby slightly contributing to planetary angular momentum.
Because the system exhibits rotational symmetry. It follows from Noether's theorem that angular momentum is conserved. Only when you include the interactions with other stellar bodies you lose the symmetry and you have an opportunity to shed angular momentum.
Sure. I'm not going to perform the computation, but my physical intuition tells me that it's completely negligible. The amount of thermal energy the earth absorbs or emits per year must be dwarfed by several orders of magnitudes compared to the rotational energy or the energy lost via tidal friction.
Like most things, nature is already doing it and has been for millions of years.