Is it normal for MY lights to briefly dim when my NEIGHBOR is using a power saw?
The dimming lights is caused by voltage dropping.  This could definitely happen from others in your neighbourhood turning on large loads.  Typically anywhere from a few houses to an entire block will share one transformer, so you are pretty much directly sharing the power with them.

If this happens frequently, contact your utility company.  They will be able to check if your neighbourhood needs upgrades to maintain a stable voltage.