Channel Divinity is described on PHB pp 58 (emphasis mine) as:
At 2nd level, you gain the ability to channel divine energy directly from your deity, using that energy to fuel magical effects: Turn Undead...
This clearly marks Channel Divinity as a magical effect, and the Magic Resistance of the Flameskull would be triggered for advantage on the saving throw for Turn Undead.
As for the 2nd question, Magical Resistance is ONLY active against:
Spells and other magical effects
If something isn't a magical effect or a spell, then Magical Resistance isn't triggered. A more complete answer can be found on your other question.