If I were to buy a house near my dream school to send my DS and it is within the 1km radius from the school. However, there is another school, let's call it school 2. School 2 is nearer to my flat than school 1. What's my chances to go into School 1?

It doesnt matter which sch is nearer if both are within 1km. What you should look out for is the historical data on the successful applications (whether you will need to ballot if you are within 1km in phase 2b or 2c) before you decide if you want to try for school 1 or 2.