I heard that as a SN striking for BM3 you can use your BM3 PQS to get basic Boat Crew qualified within roughly a few months (depending on your work, studying, etc.) and then within another couple months can finish the BM3 PQS and be ready to make third. Is this what most strikers do?

Get your boat crew cert and pass the DWO exam and you'll be well on your way to making BM3. I would recommend studying for the DWO exam now as that is what holds up most BM strikers from advancing.

Yes there are a big chunk of practical factors in the BM3 PQS that are basically tasks ripped from the Boat Crew PQS. And yes, get cracking on that DWO.