What should I expect during a first class medical examination?
You can see the requirements for all FAA medicals in 14 CFR 67. 

Specifically, Subpart C (67.2xx) deals with second class medicals and Subpart B (67.1xx) deals with first class medicals.  

The only difference my cursory read of these regulations revealed is:


x.111 - Cardiovascular. A first class medical requires EKG after your 35th birthday and every year after age 40.


This leads me to believe any real differences are likely in the ME's guidelines for issuing the medical, and I am not familiar with those.

The only other differences relate to duration and requirement for the exercise of privileges. 

On your second question, if you apply for a first class medical and for some reason could not qualify for one, you will be denied or deferred even if you could hold a lower class medical (this is also true of a second class application).  The only possibilities at the end of a medical exam are walking out with a medical of the class you applied for or walking out without a medical.  There is no fallthrough to a lower class.

If you have an issue that you believe would inhibit your ability to get a first class medical, an avenue to explore this is through AOPA where you can talk with a doctor and get advice on your ability to pass a medical and support in handling a deferred medical application.