Level 1 of Tenebrium allows you to handle tenebrium without getting Rot. Level 3 allows you to drag a Tenebrium bar onto a weapon to add tenebrium damage (someone reported that if you drag the weapon onto the bar you only need level 1). There is no benefit to boosting Tenebrium above level 3.

As for quests, talk to Brandon in Silverglen and listen to his plan; if you tell him you don't want to talk about it, he will not bring it up again. There is an alternate way to learn the Tenebrium ability,
a book in Sacred Stone.