Long term lurker, first time poster (hello!) coming on to post as I grew up in T Heath (near the dreaded pond that isn't a pond) and occasionally go back now and then for the football and to see friends.
On the green space front I wouldn't worry too much - Grangewood Park is nice (my dad used to live opposite) there's also (if they haven't disappeared) Trumble Gardens and the Recreation Ground which were all places I and my friends played in as kids. Crystal Palace Park and S Norwood Country Park also close if you have a car.
Activities for kids include the library and the recently rebuilt swimming pool, and there's probably more going on than that I don't know about. Teens - less good, but there's shopping/cinema in central Croydon a short bus ride away. Have to admit that as I got older and came back for visits from university the main appeal was that central London was 20 mins away by train.
I never felt/feel scared walking around in the day but occasionally did feel a bit worried at night as a older teenager after a bit of catcalling on the street, but in my experience that can happen in any part of London, sadly. The worst we had was a couple of break ins.
Community wise, it's hard to say what it's like now, but I remember knowing a fair few of our neighbours, and when my mum sadly passed away and I was sorting her house and funeral a few people came up to me on the street and gave their condolences, which meant a lot. We also held her wake in her local pub and lots of people dropped in.
The High Street is pretty awful though!
Should also add the caveat that I haven't lived there fulltime for (counts) around 14 years, but I thought you might want reassurance that kids can grow up there with no obvious ill effects.