1. Yes! Only on non-critical work.
2. Yes! Even on critical work.
3. No! Focus on manager duties.
4. Depends (comment below)
Chhose and explain.
I didn't do anything terribly difficult/deep, but I think it conveyed a strong, empathetic connection to what they were dealing with that mattered to them.
e.g. You need an internal dashboard but your teams are busy working on customer-facing features? You write it.
One time we suddenly and urgently needed to start caching responses from an external service. My manager wrote something simple in a day or two. Meant that the team didn’t get distracted from the more complex work we were doing.