On character cards change the "Talents" info tab to "Advanced Stats" and include Crit Chance, Mana Boost, and Plus Healing Received stats

This information being readily available would be super helpful in choosing emblem paths and troops to use.

No bad idea. But hero card only shows the stats without troops. There is no healing bonus and no crit bonus on heroes without troops, only mana from talent nodes and costumes.

But it requires that you must assign a troop to your hero card. Problem here, what should be shown, when your hero is in different teams with different troops assigned. What shall be shown, when the hero is in no team?

Maybe we need an extended view on each hero, where you can apply different troops without changing any teams.
In that case I would also like to see the troop modified DoT.

EDIT:
Possible solution after thinking more about it.
Show those additional stats only when you hit the question mark when you are in the team edit mode

I was thinking of those problems too, and I, like you, thought they could be shown when in Team Edit, but also I thought that when not in Team Edit it would just show the non-troop numbers.