Vex, Cheerless

Yes, while Vex is in combat, she adds 1 to an enemy spell played from face down before discounts are applied.

Playing a card from face down ignores its base cost,^811.1.b but Vex's increase is applied afterward.^356.1.b.3 Additional costs or other increases can raise the spell's cost further, and later discounts can reduce it.^{356.2356.3356.4} This increase does not apply to units or gear played from face down because Vex modifies only spell costs.

Yes, while Vex is in combat, her discount applies to [Deflect] costs when your spell targets an opponent's permanent.

[Deflect] is a mandatory additional cost.^356.2.a.2 When your spell targets an opponent's permanent with [Deflect], that additional cost is added before Vex's discount is applied.^{809.1.d356.2356.4}

Vex's discount can offset resources added by [Deflect] because discounts can reduce additional costs.^356.4.f Vex's discount cannot reduce the spell's cost below Vex's printed minimum of 1, but another total-cost discount applied afterward can reduce it further.^{356.4.d.1356.4.e}