Q: Best class and race for tank healer in eso?

Definitely Templar class, Breton race, without a doubt.

Templars have a multitude of healing abilities, and are absolutely the best healers in the game (despite other classes thinking they are equals). They are the only ones with a single-target direct heal that can crit for huge amounts, and while it’s the most used and useful ability in their arsenal they also have 5 other amazing healing spells.

Breton is the best race for a healer, due to the passive ability that reduced magicka cost of spells. That particular stat is very hard to come by otherwise, and 3% can make a significant difference especially when you stack it with other bonuses.

Relevant: Templar guide, Racial bonuses.