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No - TIE fighters don't have any shields. However, TIE interceptors might be able to.
Yes, they can - At least, they're mentioned as being able to land on planets in the comics and books. TIE Fighters (and Interceptors) are generally entered through a hatch in the roof of the cockpit so they usually dock within ships, attached to docking racks that allow entrance from above. However, they can certainly be landed on planets and used by the local Imperial forces.
Of course it would already have to be in the atmosphere, since it's far too small to not burn up on re-entry. This is something that bothered me regarding rebel craft because they are also too small, then again they have shields so maybe they protect from heat.