1. If a character is suffering from an effect that makes it lose its icons for a whole phase, can it use another effect to re-gain the lost icon(s) during that same phase?

2. What if the character is under a constant lose icon and a constant gain icon effect (e.g. Viper's Rage vs The Builders)? Would it re-gain its icon(s) while suffering from the effect that causes it to lose its icon(s)?

Not too sure if this has been asked before, but I am unable to find an answer for it.

Thanks in advance.

Relevant card text:

The Builders
Type: Agenda House: Neutral
Cost: 1
The North.
You may run any number of The North agendas. You need 2 additional power to win the game.
Night's Watch characters you control gain a Power icon.

The Viper's Rage
Type: Event House: Martell
House Martell only.
Response: After you lose a challenge by 4 or more total STR as the defender, all characters controlled by the attacker lose a Military, an Intrigue, and a Power icon until the end of the phase.

Effects that add or remove icons, or keywords are additive.

In this case, it depends on the character you are referring to. Did he have a power icon to begin with? If so, he retains it. If he did not, however, he would add a power icon, then lose it, and zero out with no power icons.

its basically +1 power icon, and -1 power icon at the same time, which ends in a net zero of power icons.