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.

My apologies for the double post.

Not sure what happened.

This is answered in the FAQ, but basically you look at the net gain or loss. If a character has a military icon, one effect makes that character lose a military icon and another gives it a military icon, the net gain/loss is 0, so the character would still have a military icon. If the character started without one, it would still have no military icon. The order in which these effects are triggered is irrelevant it's just like strength boosts/reductions, you add all modifiers from scratch (each time a new modifier applies) and apply the net gain/loss.

The entry in the FAQ just makes it clear that the rules for multiple lasting effects outlined in the Core Set Rulebook apply to everything, not just STR:

Lasting Effects Conflict
Even if not triggered at the same time, multiple
Lasting Effects may affect the same card
at the same time. For example: a character
without the Power icon is affected by two lasting
effects. One (such as Slander) removes
a Power icon from the character, and one
(such as Lordship) adds the Power icon to
that character. In this example the two lasting
effects cancel each other, and the character is
left unchanged. The order in which the lasting
effects take place is irrelevant: the net sum
result of all lasting effects is applied to the
character (the net sum of -1 Power icon and
+1 Power icon is 0, thus the character remains
unchanged).