Hi answers:
interesting post - but most interestingly you have left out 'TEACHERS' in this.
So my DD1 goes to our local school and two great pals from nursery, who are still close friends, go to schools 1 mile away either direction. There schools have all sorts of things going on:
School A: has optional homework scheme. Each child is expected to do at least one homework of 3 possible homeworks in maths/ science/ English - they have 95% uptake on all 3 homework possibilities. Parents don't expect detailed marking - but teachers do check over all work, record who is doing it and generally check for effort and about once a month might go through a piece of homework (usually in child's weakest area) in detail, giving feedback/ hints on how to improve work next time. Oh a reading is just presumed to be going on - often writing work will feed into what the child is currently reading - but is so loosely general that it will apply to any book at all.
Our School: there is a homework policy - in theory KS2 upper have 2.5 hours of homework a week. 2 hours of which is independent reading. KS2 upper does not send home guided reading books (issues over lost books) and library books are not regularly sent home - so to achieve this many parents have to use local library or buy in books. 1 photocopied (usually Heinemann maths) worksheet (maybe 10 minutes), a short grammar/ punctuation worksheet (again maybe 10 minutes) and a short writing task related to reading (find happy/ sad words; write about favourite character; draw a new cover illustration, etc....).
School C: this school goes in for projects. So Y6 are doing WW2 and they're asked to interview family/ friends about their WW2 experiences or their parents experiences. They can then create a web page or poster about the war in XXXXX city - they had 2 weeks to do this. The school also had residents of a nearby old folks home come and talk to the kids about life in XXXX city during the war - children in care/ without family were allowed to further interview the visitors about WW2 for their homework. Y6 field trip to Bletchley Park. One homework included inventing a code - shifted alphabet code for a particular sentence given by the teacher (there were 4 possible sentences). Children then formed teams and were asked to try and crack the codes (knowing these 4 possible sentences). They also used the Bletchley Park visit to explore binary code & had maths homework working out what a number was in binary code. children were reading Goodnight Mr. Tom for guided reading during WW2 unit & went to see it performed at local theatre.
Now of course the HT has general oversight of curriculum - but what seems to be going on here is the two other schools (School A is outstanding and School C is rated GOOD) - give their teachers a lot of leeway in delivery of curriculum. There also seems to be a lot of cross-fertilisation: visit/ special events link in well with current curriculum which feeds into writing/ reading/ maths.
So personally - I don't think parents have a lot to do with this - they support it, encourage their children to work hard/ do homework, but they aren't dictating this or that is delivered. They are praising the school & giving lots of positive feedback of course. The PTA at School C is dire - it keeps collapsing - but the school gets round it with dress up days, class bake sales, etc... and doesn't sweat it if they can't organize a summer fair. Doesn't seem to affect things.
In terms of your issues:
playground: often schools can't really control size/ quality of playground - depends when it was built/ if the council sold of land/ what funds they have access to as a school for improvements (and if they have other higher priorities - leaky flat roof for example).
swimming: our school goes in for 5 full afternoons of swimming for two weeks - kids are exhausted but really enjoy it. Easier because pool is off site - so a bit of a logistical issue for the school - traffic problems mean getting back for 3:30 can be a struggle.
special activities for high ability children: I think this is feeding through. I get the impression that OFSTED are big on differentiated learning and showing more than expected progress in all achievers - not just low achievers. In other words - previously schools may have seen improving low achievers performance was a priority because they were rewarded in a number of ways (OFSTED/ good KS2 SATs results/ good CVA score/ etc...) - now OFSTED is checking by each band of ability: low ability/ average ability/ high ability.
One problem I do find with this is that often our school is approached about some special event: science competition/ writing workshop/ theatre production - but there are only 5-6 places per school. I know that parents have complained that no boys were asked or that their child is on top table but wasn't asked, etc.... I think limited numbers often puts schools in a difficult situation. Certainly my DD is going to an event solely because the bright sparks who normally go were off taking a private school entrance exam, so she was asked at the last minute. We're glad she was asked - and are sure it will be of benefit.
Our school seriously suffers from a mentality of only 5 or 6 pupils are 'top table'/ highest ability. Often leaving out one or two who clearly are as able as the 'top table' group. I really think it's these children - often quieter, possibly with less pushy parents - who are losing out at our school.
In terms of staffing - full-time TA's or not - I think this is down to the HT and their budget. If they're spending a lot on tutors for FSM pupils (to close the gap) which can be as much at £50 an hour - they may be really struggling to afford 1 TA per class. Also I think the benefits of TAs are somewhat questionable - our school has all shads: former teachers who want less stress but are fantastic and achieve great things to former dinner ladies - lovely, helpful but taught DD1 to say 'ain't' and have marked maths work wrong, when it was correct.
Personally I think what schools achieve is down to how they function as a team. If it's a team where SMT plays individuals to their strengths and where staff feel they can input on planning/ curriculum/ etc... and make changes - tends to be effective school. If it's a team (like our school) where a select few hold the reigns of power and the rest are marginalized/ overlooked - it can lead to a very bad atmosphere - and higher teacher turnover - we've lost 8 teachers in as many years - single form school.
Our school seems to be endlessly on their back foot - behind with the times on what best practice is and unclear what to do in regard to new initiatives (i.e. have yet to adopt new curriculum - only announced Y6 SPAG test in April 2013 for Y6 that year, claiming it had only just been announced, which definitely wasn't the case and many parents were asking the school what preparation they were making for it).