Brand new Alternator will not turn?

It looks like the new pulley is just too clean and shiny to see that it is spinning. If the belt was slipping over that pulley, you'd know it right away by the loud squeal.

A quick simple test you can do is to watch the brightness of the headlights. If they dim a little when you stop the engine, the generator is working. The better test is to measure the battery's voltage with the engine running. It should be between 13.75 and 14.75 volts. If you're not familiar with using a digital voltmeter, check out this article first:

https://www.2carpros.com/articles/how-to-use-a-voltmeter

They're showing an auto-ranging meter. That's an expensive feature you don't have to have. You can find perfectly fine meters at Walmart, any hardware store, or a nice one at Harbor Freight Tools for $7.00. I can help you set it up if needed.

If you think I overlooked something, put a white mark on the pulley with paint or chalk. That will make it easier to see when the engine is running.

This article explains part of the charging system tests:

https://www.2carpros.com/articles/how-to-check-a-car-alternator

Be aware this is just the first step. Most of the time, if this test comes out okay, that's all you need to do. When you're having other problems, particularly the battery slowly running down over days or weeks, the rest of the tests are required, but those require a professional load tester. The tests take just a couple of minutes. I can describe them further if needed.

12.5 volts with the engine not running indicates the battery is just a little discharged, but not by much. A good, fully-charged battery will read 12.6 volts. 12.5 volts after starting the engine indicates the charging system is dead. Voltage now should be between 13.75 and 14.75 volts. It also suggests the battery is in pretty good condition. Normally the vehicle's electrical system will draw that voltage down more when the charging system isn't working.

The 16.1 and 15.8A confuses me. Is that amps? Where and how did you measure that?

If there's a diagnostic fault code set, find the exact code number and tell me that. You can also go here:

https://www.2carpros.com/trouble_codes/obd2

to see the definitions, or I can interpret them for you. This code could have something to do with the belt being misrouted the first time. If the generator wasn't spinning with the engine running, that would be detected and the code would be set, but simply fixing the problem doesn't make the code go away. On some car brands the code will self-erase over time, but that typically takes up to 50 engine starts. Otherwise, you have to erase the codes yourself. Your code reader might be capable of doing that. If you can erase the codes, do so, then see if any set again. That will give us a dandy starting point.