Well, you may not have to worry, but if you have large unpoured areas on a design with a professional PCB manufacturer (of the traditional, high-touch kind), they will ask if you want to pour some copper there. Reason being that it makes the process faster, more consistent and reduce possible side-etching on lanes. It may not a make a difference in most cases, but you may just save some time and effort by doing this.
Yes, but this costs pales in the cost of redoing in case of problems with side-etching and the overall tightened manufacturing constraints.
And yes, they get to recover the copper, at the very least to make treatment easier for discarding (copper is a very bad pollutant). But not only there's a cost, this is dealt with by waste treatment companies that will at most use the copper value to recoup some of the cost of the treatment.
