Do the amount of times a wire is coiled in a coil play a factor in how much power is generated, and if so, how? Do the circumference of the coils play a factor in how much power is generated, and if so, how?
Does the gauge of the wire play a factor in how much power is generated, and if so, how?
Do the amount of coils play a factor in how much power is generated, and if so, how?
Do the amount or size or strength of the magnets play a factor in how much power is generated, and if so, how?

I know these are a lot of questions but any and all help in the matter would truly be appreciated!! Thank you!

A lot of these questions are somewhat subjective as to the construction of the generator. What is this for?

I want to build a 12v DC induction generator but I also want to experiment on a larger scale in the future which is why I'm trying to understand the fundamentals. Thank you for helping.