Stupid question regarding Hailstorm helixes

So I played Montana during the Technical/Beta and didn’t like him at all. In trying him now I’m rank 8 and honestly quite loving him. Probably has to do with my gear and how I kinda know more how to play BattleBorn

My question is about his Helixes and Hailstorm skill. I’m liking his “Firestorm” helix which turns Hailstorm into “Firestorm”

Now my question from here on is does the helixes thereafter that say “Hailstorm” apply to my newly added “Firestorm” or not?

For example: “Firestorm” is level 4. His level 6 mutation states
"Hailstorm bullets penetrate multiple targets"
His level 7 right helix states “Increases Hailstorm’s skill duration”

It specifically states “Hailstorm” but since I turned it into “Firestorm” does it still get the buffs or only if I keep it as a Freeze Gun?

Also my big concern is his level 9 helix/mutation which states
"Increases Hailstorm damage reduction by 25%"
“Increases Minigun damage while HAILSTORM is active”

So these only apply if I keep the Freeze Gun debuff - correct?

Yeah, it’s confusing, but yes, the skill is still called Hailstorm (if you check the description of the Firestorm helix upgrade, the skill is still referred to as Hailstorm), so anything that affects Hailstorm still affects that skill.
You’ll notice the only other helix upgrade that specifically alters Hailstorm’s slowing effect (Bullet-Buff, at 9) goes on to state that if you should have the Firestorm upgrade it’s damage-over-time effects are lengthened instead.