Generally, in some indoor stadiums or arenas or theaters, if you will…there is a walkable space in the roof or the area directly above the stage…from which many technical activities are performed…
Learn English – the name for the walkable area above a stadium
single-word-requests
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It's not that the words synchronous and asynchronous are "too technical" for the intended meanings - they're simply the wrong words to describe interaction between people (though they are standard terminology for the two different types of communication between electronic devices).
The normal term for what OP calls "synchronous" is [real-time] interactive. I can't think of a standard word for the opposite, but perhaps something based on delayed response would do.
Per @cindi's comment below, non-interactive is a perfectly good term for person-to-person communication where any response is so long delayed it's not meaningful to speak of, for example, the flow of conversation.
In British English, at least, this is often called a recreation ground. This also seems to fit your description of being in "...bad shape, like missing turf or torn goal nets." as a lot of them are just mown fields, with basic facilities like a couple of goal posts etc.
Colloquially it may be shortened to rec or rec ground in some areas. I think this best reflects the description of somewhere where you would go just to "kick around" like you would on a German Bolzplatz. E.g. "let's go have a kick-about on the rec."
ADDITION:
@Steve – you have swayed me to playing fields, which I get the feeling is a more widely used term in English in general.
Best Answer
The general term you might refer to is Catwalk, but there must be a specific term for stage.