Have you tried? I've certainly been able to. And I'm definitely not alone in having used those facilities. I've used them personally and for ad-hoc sport events (lacrosse isn't exactly popular in the area I'm in right now).
Not recently, though I have observed locked doors and gates that make it pretty difficult to use. If your caveat is you need to call ahead to organize an event that's a pretty different use-case from what I'd like to do, which is to use them very casually and occasionally.
I've never called ahead or anything like that. There are a fair amount of people using them on the weekends, as far as I've seen.
There is one school that definitely is gated off, but that's because it's near a major point of interest and I can only assume they're worried about non-community members damaging the property.
