You are correct. Week 3 is 5-3-1+
There are many flavors of 531 from the old book and there is a new 2nd version out as well (since the 1st one got pirated on smart phones and Jim decided to update a lot of it).
In 2011 I ran 5 cycles of 531 from Feb-Aug. Maybe it was 6. There was a back injury in there.
I used a 2day split for the first 2 cycles. Eventually I added in FrontSquat and GoodMornings so it was 3 lifts per day for 1 or 2 cycles and eventually split that into a 3rd day where I would go in and do DB assistance work and DB complexes.
Whether to include more PC work depends on the type of squat you may be using. GluteHamRaises if you have access one would be good or RDL's.
I mainly kept to a simple no assistance version of 531 as I was in the gym tumbling and working events 5d/week besides my time being limited. Getting in and doing 2 or 3 lifts and getting out was very doable in 45 minutes to an hour.