Am I allowed to wash my car during this CB period? As I stay in an old flat with only open carpark, my car has become quite dirty. So am wondering if possible to drive to a nearby multistorey to wash?

Same problem! Generally, there is no restriction on washing your car so long as you observe the current circuit breaker measures, e.g. wearing a mask when outside.

However, I'm not sure how feasible it will be to wash your car with a mask on (e.g. may be tiring and difficult to breathe).

Alternatively, you may consider sending it to the nearby car wash (though I don't usually do it for my own car; but well, some sacrifices here and there).