Clarification on washing meat and dairy dishes in sink and dishwasher

Kashrut
1

I would like clarification on the above topic to make sure I don’t make a mistake.

1 So I can wash meat and dairy dishes in the same dishwasher and don’t need separate loads or run an empty load in between meat and dairy

2 I can wash meat and dairy dishes together in the same sink and son’t need a separate rack or dishpan for each . Do I need different sponges?

2

Correct, same time in dishwasher or sink and same sponge. All ok.