I don't know much about Park Street but that won't stop me from joining in :)
I would be very surprised if religion plays any part in Park Street's admission process. As a church school they, I think, can set their own admission criteria but most church schools (in Cambridge) don't; they rely on the local authority to set the 'rules'. Exceptions are the catholic primary schools who do take into account whether you go to church or not.
What is more important is how close you are to the school. I know a few children who go to Park St who do not live in catchment but they all live quite close to the school.
Most primary schools in Cambridge are becoming oversubscribed now (for demographics reasons) so your 'choice' is limited. If you're in catchment you're likely to get in but it's no guarantee. Schools that are considered to be very good attract more families into the catchment area, meaning not all of them can get into the school. I don't know if this has ever happened in Newnham or not.
WRT siblings, I know families that have a child in one school, have moved out of catchment and then couldn't get their next child into the same school. Conversely, I know families who have done the same and still managed to get their child's sibling into the same school. It depends on what the applications are like each year.
Not sure about the head, there was some discussion on here a while back about Newnham.
Suffice to say, you're doing the right thing by visiting the schools to see what they're like. That's probably the most important thing.
HTH :)