Mage Disintegrate and Wand/Staff Mastery with Elemental Dmg

How do skills that buff wand and staff damage interact with pure elemental wands and staves? If I "add 2 damage" to a staff which is 100% fire damage, does that added damage become fire or become physical?

Secondly, what would happen in that case if a wand or staff has base physical damage with added elemental damage (say, 3-7 physical with 3 extra ice damage)?

This seems like something someone would have asked or answered elsewhere, but I couldn't find any other posts about it using the keywords I thought most applicable.

If a staff/wand has an attack of a certain nature, every attack boost further increases the nature damage of the attack by contributing towards it. That being said, disintegrate adds only normal damage towards it, whatever the nature may be.

Great question, answered above so it seems.

The Combat Log is your go-to friend for damage details. The different damage types, physical, fire, shock, poison, etc, each get their own line in the combat log so it will show what type of damage you're doing (and if the enemy is strong or weak against it as it will show increases or decreases to the damage)