Lots of questions 
From experience, does a pre-school help with social skills/education/behaviour before primary school? Or is it not particularly necessary?
In my opinion, and experience, yes, it is good for little ones to go to some form of Nursery provision before starting school - can be playgroup or Pre-school or Nursery - the names are interchangeable. What it gives them is the experience of getting used to being 'one of a group' - that sometimes you have to wait a moment for attention; that there is a routine to the day and sometimes 'it is time to do X/Y/Z' even though that might not be what you want to do; that toys and activities need to be shared; that sometimes you have to either wait for your turn with something or that you have to finish using it before you want to as it is someone else's turn; that sometimes it is noisy; how to interact with other people your age.
is it possible to apply for primary school places this early on? No. Not if your child is going to state school. If they go to state school, they start the September after they are 4 years old. You have to apply before the deadline (currently the 15th January in the year before they start in September). That is school . Some schools do have a Nursery class, and the admission arrangements for that are different. Attending the Nursery or not doesn't affect whether they get a place in Reception though.
However, some people (around 7% of the population I believe) choose to pay privately for Education. I don't know much about this, but someone will no doubt be along soon who does. Admission for Private school is completely different, and I believe you can put your name down when they are babies, for some schools.
What 'good' criteria should a primary school be judged by?
That is really very much 'opinion'. Subjective rather than objective. IMO, the best thing is to talk to other local people (and get lots of opinions - one bad experience doesn't make a bad school, and one glowing one doesn't make a great school); also look at the text of the OFSTED report - see how old it is, and read what it is they might be being marked down (or up) on - some is less important than other things.; also go and look round, you can pick up a real 'feel' for a school when you look round.