First:
I agree with the despair thing. It looks a little weird, that this didnt support the new gauge.

Aside of that:

MP reg)
Whe will have or normal mp reg.
Why are all people saying, that the BLM would be the only class, who would be able to regenerate the mp like every other class is doing it.

What changed is simply, that the naturaly regeneration isnt as strong as before anymore.
In exchange, is the skill regeneration even stronger and probably even faster as before. As long as whe dont have 0 Mp, is it completly meaningless, how slow the naturaly mp regeneration would be. Because: After a few ice spells, would whe have max mp ready.
And have whe very low mp, is there the other skill to strenght the mp regeneration over time. Who every other caster has to.
BLM is the caster, who has the less problems with mana regeneration. And i dont think, that it will change now.

Paradox)
They probably doesnt removed it from the ice phase, to hurt non-standard. Or, because it would be "to strong".
Its probably removed, because it doesnt had any propose left.

Whe needed some attacks for the ice phase, to have something to do, until the mp was ready. Having a strong skill was a nice thing and helped to hold the timer up. Fopr the phase itself was Paradox mostly weak. Because it filled only 1 soul point.
But now, do whe only need 2 attacks to finish the whole ice phase. Blizzard is creating instantly the 3 souls. And Freeze is creating the ice shards. And gives us max mp, because of the 3 ice souls. After that, have whe no reasons anymore, to stay in the ice phase. Except of downtime, when whe are not able to attack the enemie in a good way (like, the meteor phase again Thal).
Because of that, is a ice Paradox questionable. Because the fire attack makes more sense than, as having 1 aadditional attack for lower dmg.

Dlare star gauge)
Is it even stated, that whe lose the stacks, when whe sswitch to the ice phase?
No yter i saw, had mentioned anything in that direction, that whe would lose the stacks (and no yter showed any scene, where you switched to ice, before used it up completly).