Some states have lemon laws for used cars. Check out laws where you live. Should have been a paper in the windows saying either as-is or with warentee. What does it say?
BMW dealer will not fight with third party extended warranty company for you. That will be your job.
You need to get a detailed list of what is wrong. Then you need to read fine print of your extended warranty. Sometimes warrentee
company can be convinced to change mind (but usually those warrantee's are written to cover only things that rarely fail). Their first response will be - no not covered - but if you read the fine print it might be covered and you just have to point it out to them.
Also if they don't call back, call them. The longer this drags out the worse chance you have.