Let's say I have Facebook Ad and it's working well with Precise targeting (phase 1). My pixel learned something already...
so I am going to "phase 2" and make BROAD interest targeting for the same product (but now my pixel has some knowledge from Phase1).
Q: On what BASIS facebook Pixel will know that I want to target similar people like in "Phase1" in order to sell the same product? Is is target URL or what? What if URL changes?
Assuming you're using a Lookalike Audience, based on people who converted as reported by your pixel. The exact data elements that Lookalike Audiences are based on is part of Facebook's secret sauce, but they can include interest and demographic data.
If the URL on which your pixel is firing changes, that's fine so long as your pixel does continue to fire and your ads are driving people to the right (new) page.