Inscription and Mirror Walk

As I understand, when a do-not-replace clause is in effect, there is one card slot/space that is “counting against” the affected Methuselah’s hand size, meaning that the Methuselah must hold one card fewer.

Question 1.a: Does the do-not-replace clause count as part of the “ability of that card” that gets used by an Inscription?

1.b: If a vampire equipped with an Inscription that has Mirror Walk on it burns and uses the Inscription, must the Methuselah then drop a card to respect the do-not-replace clause on Mirror Walk?

1.c (if no to 1.a/1.b): Does anything else happen that might seem unusual or unexpected with respect to the Methuselah’s effective hand size at any point in time (e.g. when the Inscription is first played)?

Question 2: I believe that using the ability of an action modifier on an Inscription does not count as playing the action modifier, such that during a single action, a vampire could burn two Inscriptions both containing Mirror Walk, and then play a Mirror Walk. Is that correct?

Thanks Much!
-Bill Troxel

Inscription
Equipment.
[tha] Put this equipment on a ready vampire and put a card that requires Thaumaturgy [tha] from your hand on it (face up, out of play; this acting vampire pays the cost of that card). The vampire with this equipment can burn this equipment to use the basic Thaumaturgy ability of that card.
[THA] As above, but the vampire can use the superior Thaumaturgy [THA] ability of the card.

Mirror Walk
Action Modifier
Do not replace until your discard phase.
[tha] +1 stealth.
[THA] As [tha] above, and if this action is blocked, the action ends (with no combat).