You can, as in this procedure: http://www.orgsyn.org/demo.aspx?prep=CV4P0984

It is standard procedure in many reactions to add a slight molar excess (e.g. 10%) of a reagent just to ensure completion of the reaction. I have not seen analyses of “bad” NBS to quantify just how high the Br2 content can get, but I would not expect it to be more than 10%.

So my short answer is no, not to any significant extent that it would impair the yield by more than 10%.

If there *is* a lot of Br2 present, two things could happen. First, if the impure NBS is just added to solution and dissolved, without adding alkene first, the Br2 that has been liberated can re-combine with succinimide (this is, after all, how NBS is formed).
If a relatively high concentration of Br2 persists, then what is more likely is that one would start to see dibromination of the alkene (i.e. addition of Br2) across the double bond, since bromination tends to be 3rd order overall, and low concentrations of Br2 avoid this side reaction.
In this case, then there would again a lower yield of the desired product, but not double addition of bromine.

If a large excess of NBS is added, then yes, it could start to be an issue.

You will need to identify what will be the kinetic and thermodynamic product. https://www.masterorganicchemistry.com/2017/03/22/reactions-of-dienes-12-and-14-addition/

Usually you want a solvent that has a reasonably high boiling point since the initiation step requires heat. Dichloromethane is pretty low boiling. You could go for dichloroethane instead. (83 C° versus 40 C°)

Yes.

Thanks Dave. Does L&R point to the original literature reference?