Since my level is only just approaching the point where I can fully participate in the Wayfarer community, I am only theoretically familiarizing myself with the rules.
In the case of the park, based on a slightly more recent aerial photo, I think that it may actually be an area independent of the kindergarten.
The seniors’ home (and the fitness station behind it) also doesn’t show such signs of sensitivity, although it’s hard to be 100% sure without taking a closer look.
If I correctly understand (based on the municipality’s website: Senior +), seniors spend their time there but do not live there. However, I have doubts about the public accessibility of the fitness station itself and I would judge it on that basis.