As long as equipped creature is attacking, it has
first strikeFirst 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. (CR 702.7) and must be blocked if able.
Equipped creature has "If a creature dying causes a triggered ability of this creature or an emblem you own to trigger, that ability triggers an additional time."
EquipEquip is an activated ability of Equipment cards. “Equip [cost]” means “[Cost]: Attach this permanent to target creature you control. Activate only as a sorcery.”
For more information about Equipment, see rule 301, “Artifacts.”
Equip abilities may further restrict what creatures may be chosen as legal targets. Such restrictions usually appear in the form “Equip [quality]” or “Equip [quality] creature.” These equip abilities may legally target only a creature that’s controlled by the player activating the ability and that has the chosen quality. Additional restrictions for an equip ability don’t restrict what the Equipment may be attached to.
If a permanent has multiple equip abilities, any of its equip abilities may be activated.
“Equip planeswalker” is a variant of the equip ability. “Equip planeswalker [cost]” means “[Cost]: Attach this permanent to target planeswalker you control as though that planeswalker were a creature. Activate only as a sorcery.” (CR 702.6)