This must have been the third time I've answered this question in 3 days - very weird.
As for rest periods - this depends on a lot of stuff, which is way beyond anything I want to type or anyone cares to read. Suffice it to say, rest periods should NOT be monitored during the beginning of this journey. Just get through the sets. Once you've done it for several weeks you can find out where your sweet spot is - but don't turn this into a conditioning workout and being the limiting factor of how much you can lift. But let's say this - 30 seconds would NOT be recommended.
Second question - NO! Your TM is increased as needed by the program NOT your PR sets. That's the worse thing you can do. Re-read the chapter about the importance of the TM (in the original book and the Beyond book). The TM set at 90% or lower is the key.