How to keep rice in a biryani from burning and sticking together?
Some options:  


Prepare the biryani in an oven (used when making biryani with uncooked meat) in a really thick, covered oven pan, with no foiling at 200 degrees Celsius for around 30 mins. It won't stick to the bottom or get burnt.  
Keep a cast iron tawa underneath the pot the rice is in. Rice won't stick.  
Add some ghee at the bottom of the rice before layering.  
Keep the heat low. "Dum"ming the biryani is steaming it rather than cooking it with high heat. You'll also need to seal the container.  


The sticky rice at the bottom is called "khurchan", and some people actually find it delicious. The burnt rice is because of the lack of liquid and the high heat. Happens mainly because the water evaporates while cooking.  

There's a similar question asked here: How do I avoid dry meat and burned masala and rice in biryana?