I've experienced 3 different times my ABS light, airbag warning light and traction control lights have come on. Slamming on the brakes proved that ABS was gone with a tire squeeling slide. The same for the traction control light. I didn't try the airbags out. I called to make an appointment with mazda to figure out what was up. The lights cleared when I shut off and restarted so mazda couldn't find anything out. They came on while doing 60 through a very tight highway interchange corner. I'm not sure if anyone else has had anything similar happen or if they'd heard of this before. Aside from coming in and clearing everything is back to normal including the traction control and ABS working like normal again.

 

Airbag light is most times just the connector which is located underneath and in the rear of the front passenger seat. Have you been moving that seat back and forth? Most times simply plugging it back in can do the trick.

As far as the others go.........how bad are your tires? Maybe those should've come on?
It could also be the sensor connectors down at the wheels though.

 

Having all of the brake lights fail will kill the whole system.

If you have LEDs in all positions (without a incandescent simulator in-line) or an intermittent lighting harness, the ABS/TCS/DSC will turn completely off!

 

just had my srs light on and unplugged and plugged back in the connectors under both seats and behind the glove box

 

I had this similar problem recently -I got ABS, traction control and handbrake lights on. I am not sure what triggered it -was driving normally. Fixed it by switching off /on the engine.
A friend of mine had the same symptoms on her 8 due to the rear tyres being of different sizes -I do not have that situation although I suspect the problem appeared after I changed to a set of new rear tyres.
I have since re-balanced the tyres and had the ABS sensors cleaned. The problem still appeared once. I have now moved my new rear tyres to the front and currently monitoring the situation.

 

so far I had no incidents with the new tyres in the front. I have since moved them back to the rear and did wheel alignment (as I had removed some underbraces and swapped in Whiteline swaybars) -now the lights come on very rarely.
I would say the cause of my problem would probably be the new tyres (tyres are not so new now as I have done more than 2000km on them).