starvation mode

how long does it takes to go into starvation mode when undereating?

1 - 3 days.

The body is incredibly effective at adapting to a certain calorie intake, particularly starvation levels.

I would say about 2 days, if you are not eating anything at all

If you are eating about 500 calories a day, then maybe around 4-5 day

so after consuming a low calorie diet for about 3 days, your body will hold on to fat?

There is still debate about what starvation mode is and whether it exists. The important factor here is that you cannot be healthy by restricting your calories by more than your body needs.

To stay healthy and shiny you need, at minimum, 1200 calories. You really don't want to gamble with that.