First strike is a static ability that modifies the rules for the combat damage step. (See rule 310, “Combat Damage Step.”)
At the start of the combat damage step, if at least one attacking or blocking creature has first strike or double strike (see rule 502.28), creatures without first strike or double strike don’t assign combat damage. Instead of proceeding to end of combat, the phase gets a second combat damage step to handle the remaining creatures. In the second combat damage step, surviving attackers and blockers that didn’t assign combat damage in the first step, plus any creatures with double strike, assign their combat damage.
Adding or removing first strike any time after combat damage has been put on the stack in the first combat damage step won’t prevent a creature from dealing combat damage or allow it to deal combat damage twice.
Multiple instances of first strike on the same creature are redundant.