Lim-Dûl's High Guard

First strike is a static ability that modifies the rules for the combat damage step. (See rule 510, “Combat Damage Step.”)

If at least one attacking or blocking creature has first strike or double strike (see rule 702.4) as the combat damage step begins, the only creatures that assign combat damage in that step are those with first strike or double strike. After that step, instead of proceeding to the end of combat step, the phase gets a second combat damage step. The only creatures that assign combat damage in that step are the remaining attackers and blockers that had neither first strike nor double strike as the first combat damage step began, as well as the remaining attackers and blockers that currently have double strike. After that step, the phase proceeds to the end of combat step.

Giving first strike to a creature without it after combat damage has already been dealt in the first combat damage step won’t preclude that creature from assigning combat damage in the second combat damage step. Removing first strike from a creature after it has already dealt combat damage in the first combat damage step won’t allow it to also assign combat damage in the second combat damage step (unless the creature has double strike).

Multiple instances of first strike on the same creature are redundant.

If the effect of a resolving spell or ability regenerates a permanent, it creates a replacement effect that protects the permanent the next time it would be destroyed this turn. In this case, “Regenerate [permanent]” means “The next time [permanent] would be destroyed this turn, instead remove all damage marked on it and its controller taps it. If it’s an attacking or blocking creature, remove it from combat.”

If the effect of a static ability regenerates a permanent, it replaces destruction with an alternate effect each time that permanent would be destroyed. In this case, “Regenerate [permanent]” means “Instead remove all damage marked on [permanent] and its controller taps it. If it’s an attacking or blocking creature, remove it from combat.”

Neither activating an ability that creates a regeneration shield nor casting a spell that creates a regeneration shield is the same as regenerating a permanent. Effects that say that a permanent can’t be regenerated don’t preclude such abilities from being activated or such spells from being cast; rather, they cause regeneration shields to not be applied.