After replacing the alternator with a new/used one the engine idles poorly and when the truck is turned off with the keys removed my battery light will stay on?

Yep, it sounds like you have a defective alternator that is allowing the voltage to back feed through it. To be sure disconnect the wiring from the alternator to see if the light goes off. Here is a generic guide to help you step by step with instructions in the diagrams below to show you how on your car:

https://www.2carpros.com/articles/how-to-replace-an-alternator

Check out the images (below). Please let us know how it goes