How do I know if a firewall and mortar contain asbestos?
To test for asbestos, you take small parts of the material and take it to (or ship it to) a testing lab. Most major metropolitan areas will have testing labs.
Remember that Asbestos is only really dangerous in high quantities, and even then, only in it's 'friable' state (meaning easily turned to dust).
If you're demo-ing a small part of your own house, odds are slim that any harm will come to you. But it wouldn't hurt to take precautions, of course. I'd suggest getting a proper mask (one rated for asbestos), a HEPA filter for your dust collection vac and wet everything down as much as you can before and during the demo process.
UPDATE:
Some of these other answers are a bit overly dramatic, IMHO. Asbestos isn't universally deadly. In fact, in many cases where you might find and remove it in a home, the actual danger to you is minimal--especially if you practice even the most rudimentary safety precautions (keep the material wet, use a HEPA filter on the shop vac, etc.)
Of course, everyone has to do their own research and come to their own conclusions. But to balance the FUD a bit, here's a bit of quoted information from this site:
http://www.naturalhandyman.com/iip/infsisters/infasbestos.html

Asbestos a not a single, easily categorized substance such as carbon monoxide or radon.  It occurs in a number of different forms and the risks posed by them vary considerably... from minimal to severe. Crocidolite and amosite asbestos, known as amphibole asbestos, are the most dangerous forms.  Their fibers cling tenaciously to lung tissue while resisting the body's natural self-cleaning processes.  This long term irritation to body tissue can lead to disease and death. Fortunately, these forms of asbestos have been banned for years though some may still exist in older homes.
Chrysotile asbestos, a less toxic form, comprises over 90% of all the asbestos used in the US.   This form of asbestos is not nearly as persistent in lung tissue and low level intermittent exposure is not considered to be a health risk to a healthy person.
In fact, both OSHA and the EPA concur that asbestos is not dangerous unless airborne.
Even if airborne, many studies of asbestos workers indicate that it takes more than a casual exposure to asbestos dust to cause disease... even over periods as long as 15 to 30 years!  Asbestos doesn't &quot;radiate&quot; danger and its mere existence in low levels in your environment is not automatically cause for alarm.

Just my opinion, but I think the stress caused by irrational asbestos fears would cause more health problems than any actual low-level exposure by a DIYer. ;)