Your dishwasher uses hot water so if you run your sink until hot water is coming out before running your dishwasher it means it’s immediately getting hot water. It’s about clearing the cold water out of your pipe.

Whether or not you can use the sink while the dishes are being washed depends on your water heater. If you can wash your hands while someone is taking a shower without blasting them with cold water then you should be fine to use your sink while the dishes are being washed.