I haven't seen anyone take the time to definitively test / confirm / mod to see whether P8 difficulty, TZ stats and unique/minion/champion effects on base life/damage are carried over into new games / locked in
The problem is these stats are often too hard to discern and you'd need something like another hostile player using a known DPS of very long poison and measuring life, otherwise need a mod that displays monster stats directly
What I can confirm trivially is that monsters are locking in at minimum some form of their level when bound, so its very likely that TZ monsters are indeed stronger, and monster variants from different zones keep their locked in stats (ie urdars in frigid highlands have 75% dr and 33% resists and ~15% extra HP)
That's simple enough, because if you take a monster bound in hell to norm it will kill everything in 1 hit and take no damage.
and obviously all their affixes including TZ affixes on normal mobs, lock in when bound and stay when joining a new game
The demon you should choose and how to farm for it depends on builds. Hephasto is great for 1 point bind builds that can't reach 20 bind demon so he's the easiest aura enchanted demon, and has a huge HP pool with no +skills. But he has 0 regen and his aura is redundant once you have level 20+ bind.
I became curious about this when I respecc'd my lcok and wondered if I should spend a Rifver of Flame TZ on a super demon
then i realized my non super demon might as well be a super demon and never thought about it again. Now im curious again though!