A miter cut is an angled cut that you’d normally use for corner pieces of molding. While a miter cut is usually fine for corners that are perfect 90-degree angles, they often aren’t enough to snugly fit molding pieces together.
If you just use miter cuts, you may have to end up filling your molding, which doesn’t look as smooth.
When you’re working with 2 corner pieces of molding, you only need to cope 1 of them.
As you encounter bends and curves in the molding, tilt your angle grinder to accommodate the wood.
While using caulk is totally fine, crown molding usually looks better if the wood is flush without any gaps. Try using caulk as a last resort.