Where does Taq polymerase migrate during electrophoresis?
Unlike in an SDS-PAGE, where the SDS adds negative charges to all proteins, in a standard agarose gel for nucleic acids all proteins should move according to their own charge.

You can get a rough idea in which direction Taq would move by getting the amino acid sequence and calculating the isoelectric point at the pH you are running your get at. It might be that the protein isn't even negatively charged at this pH, then it would move in the opposite direction of the DNA out of the gel.

An exact prediction is rather hard, as it depends on the shape and size of the protein, the pore size in the agarose gel and the exact charge. It is not as simple as for DNA. You would have to just try it out to get an accurate value.

You can use any common method of staining proteins like Coomassie.

I think reusing the Taq is very unrealistic. It is still pretty stable at higher temperatures, so it will probably survive the temperatures the gel is running at. I would guess that you lose so much during PCR, gel and purification that it would not be worth the effort. And you would need to purify it extremely well, unless you want to amplify the same DNA in all your future PCR reactions. Any DNA contamination left from your gel might interfere with your later reactions.

If you require a very large amount of Taq and want to cut costs, I'd rather try and produce and purify the enzyme yourself. That should save you a lot of money if you really use a lot of it, but it is likely not worth it on a small scale.