Both are correct.

Yes, "just" in the sentence "I just went for a run" can have both meanings, depending on the context: 1. A short time ago: * It means you went for a run very recently. * Example: "I just went for a run, so I'm still a little tired." 2. Only (nothing else): * It means the run is the only thing you did, emphasizing simplicity or exclusivity. * Example: "I just went for a run; I didn’t do any other exercise." Context determines which meaning applies. If the focus is on time, it means "a short time ago." If the focus is on activity, it means "only."

'A short time ago' is correct.

Yes, both interpretations are correct! Good job.

It can mean both “a short time ago” and “only”.