Bmw 540i overheating/heat issue

Okay so I just purchased my first car yesterday and I'm very excited to say the least. It's a 2000 540i and i bought it as is so there are a couple things that I need to fix. I have little to no experience maintaining or repairing cars but you have to start somewhere. I believe that the car has a coolant leak becuase while it is running I smell burnt coolant but i have no idea how to locate it. Also the heat does not work at all the display shows that it is on but nothing will come out. However the front defrost will turn on and put out a little air which really confuses me. Any help will be appreciated.

Sounds like you have 2 problems.
1) a bad FSU that is the speed controller for the blower motor.
2) air in the cooling system that needs to be bleed out.
When the engine is cold disconnect the top radiator hose and pour coolant into it until it won't take any more. Do the same to the top hose connection on the radiator..
After they are both full quickly connect the hose to the radiator.
Check the coolant level in the expansion tank after the engine has been run and then cooled down.