Say I have an LPVO that's dials are 1 click = 1/2 MOA. Say I'm zero'd for 50 yards but want to change to a 100 yard zero. How do I calculate how many clicks it'd take? And which direction would I even dial towards?

Secondly, a lot of people say for example a 25/300 yard zero is best! But that second number, how can you know that's where any given bullet would arc? Like a 25 yard zero is accurate again at 300 yards.. but would using different types of rifles/bullets change the trajectory, making it possible to have a 25/500 zero? How could a .22 short and a 338 Lapua have the same ballistic arc?

The real answer is you figure it out. The actual adjustment will depend on your actual drop which is specific to your load. If it needs to move approx an inch at 100 that's two clicks. For the 25/300 zero ideally you do the initial at 25 and then confirm it at 300. They are made to be solid easy to set up zero's that work well in the field. Hunters do similar stuff so they can aim and shoot quickly and know they are close to where they need to be.

The reason it works is that most common battle loads are all pretty close ballistically. The key is fine tuning everything for your setup.

Easiest way to answer those questions, work up a load, get accurate velocity numbers for it, and run them thru a good ballistics calculator, it will give you the inches/moa/mil adjustment needed for any range you want to go out to...

This is a very good one, and it has lots of options to get exactly what you want info wise...

https://www.jbmballistics.com/cgi-bin/jbmtraj-5.1.cgi

Read up on the concept of "Point Blank Range".  

Maximum Point Blank Range YouTube video HERE.

You would have to know the exact relationship between the axis of the bore and the axis of the optic, and I suspect even then it would have variables you can't account for, like the fact that dials on plenty of scopes aren't totally accurate.

Just one example is the height above bore of the optic would change the answer from one height to another.

The real answer is you take it to a range and figure it out.

No one has claimed that they would.  Sounds more like you're trolling than looking for accurate information.

..

You need to learn some things. Topics like line of sight vs. bullet position, trigonometry, gravity, time of flight, near zero vs far zero, max point blank range, etc... I'd start with a pencil and some paper and a ruler and start drawing to model for yourself the relationship between the path of the bullet and the line of sight.

/me walks out.