Zeroing your weapon is a critical part of having your kit maintained and squared away. There are lots of different thoughts on zeroing schemes. For a 5.56x45mm carbine a 50m zero is a good standard, for sidearms 25m. There are good reasons to do other things and more advanced zeroes to select for a specific gun or ammunition type. If you know how to do that, you should do that - such as ballistic point blank zeroing. It is a good idea that across your weapons you have the same scheme. That way you do not need to memorize lots of different holds and your instinctual shooting will work across all of your weapons. If you zero one AR as 50&200, don’t do a different AR at 25&300. Exception would be if you have something like an ACOG with a Bullet Drop Scale, zero that at the range specified by the manual (usually 100m). Different chamberings will have different trajectories, so it is fine to have your .30-06 hunting rifle as a 100&300 zero, and your AR as 50&200 as your brain is going to know for sure those are different guns and the holds are different.
Zeroing should be performed periodically to confirm your zero is where you think it is. Any time your optic or barrel takes a significant whack or is dropped, zero should be re-confirmed. Usually it will be fine, but, it’s better to know than assume.
If you have co-witnessing backup irons (either absolute or lower third), you can speed things up by zeroing your optic first then set your irons to match the optic. If it’s lower third and your optic is “parallax free” you will need to drop your head so the dot moves to the plane of the sights. You should then confirm your zero with your irons with the optic turned off but still in place. If you have truly backup sights that involve removing the optic to use them (some ACOG and LPVO configurations) you will need to set zero on your irons first, put your optic on the rail then zero that. No shortcuts there. Be sure that optic is on a quick release mount otherwise those backup sights are useless as you won’t be able to quickly strip the optic from the gun if necessary. If you have a magnifier for a zero power optic you should confirm that zero is the same through the magnifier as it is through the optic alone. Another shortcut if you have a super stable base that doesn’t require you touch the gun to hold the weapon on target: One can fire a few rounds, place the gun to aim at the exact place that was fired at, now without touching the gun the reticle on the optic can be moved to match the point of impact. Next rounds fired should be on target. It is very very easy to bump the gun or otherwise try to adjust the optic by aiming while doing this and of course this won’t work if that happens.
Any time you remove or move your sights or optic you need to re-zero the weapon. Many mounting systems boast return to zero on re-mount, but that makes your confirmation of zero easier. It is not to be trusted.
Variation between ammo (even round to round in the same box) will cause the point of impact to be slightly different round to round so getting each round pinpoint stacked on top of each other on your bullseye stacked on top of one another is unnecessary and probably not going to happen. If all of the hits are inside a 3” diameter circle at 50 yards averaging to the center of that circle that’s good enough. If you’re inside a 1” circle you’re good to go. You absolutely can be more precise, but understand that may be a maddening exercise depending on the stability of your rest, your skill, and quality of your rifle and ammo.
On rifles it is important to zero with the ammunition that you will actually use in a defensive situation (or in the field in the case of hunting), and deal with the zero difference when practicing on the range. 55gr FMJ practice ammo has a different zero than 77gr OTM defensive ammo (the 77gr will generally hit lower as it is flying slower). For 0-100m good enough for defensive purposes zeroing you can get away with using same bullet weights if the manufacturer stated velocities are also very similar. For example if you’re going to use 62gr M855 as your defensive ammo, you could zero with 62gr PSP provided both have a similar muzzle velocity, then confirm with the actual round.