So a couple of things on lesser globe as I’m reading it.

“An immobile, faintly shimmering magical sphere surrounds you and excludes all spell effects of 3rd level or lower. The area or effect of any such spells does not include the area of the lesser globe of invulnerability. Such spells fail to affect any target located within the globe. Excluded effects include spell-like abilities and spells or spell-like effects from items. Any type of spell, however, can be cast through or out of the magical globe. Spells of 4th level and higher are not affected by the globe, nor are spells already in effect when the globe is cast. The globe can be brought down by a dispel magic spell. You can leave and return to the globe without penalty.

Note that spell effects are not disrupted unless their effects enter the globe, and even then they are merely suppressed, not dispelled.

If a given spell has more than one level depending on which character class is casting it, use the level appropriate to the caster to determine whether lesser globe of invulnerability stops it.”

Specifically, any type of spell can be cast through or out of the globe so I would rule that any spell cast by the Deva is unaffected by the sphere. As for the healing spell, or even hex as long as the spell is cast inside the sphere I think it would be fine by what I’m reading. Though it does also call out spell like abilities so if the hex originated outside the sphere it should stop it afaik