What is the crowd's opinion of iD?

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Nests are 100% dependent on OSM data, so when they decide to update nests again, it will be global and people will notice and post about it here. The last time they update nests (and other stuff that depends on OSM) was around January this year. If your local park is not a nest, then it isn't marked as leisure=park or as any other OSM tags that becomes a nest. Check OSM data in http://ideditor.com/ whether it was changed in the last year and if it isn't marked as leisure=park and is suitable for this tag, then add it yourself. Then you just need to wait :-).

We have a field nearby that is also a nest (all fields are), but only two spawnpoints. So I added a path that is there and wasn't mapped yet and one day, they will update their data and probably add spawnpoints along that path which will become part of the nest (if they happen to be inside the field).

This is not how this works. Tags are not visible on the standard map (the link you provided). But all areas have tags nonetheless. You can explore the tags using http://ideditor.com/. You can also query these tags using http://overpass-turbo.eu. There is plenty to learn :-).

It might just be solved [1] [2]
The last one also depends on how good the Map is, feel free to check, the web browser integrated editor is really easy to use.