Car Will Not Start problems of the 2012 Mazda MAZDA3

More that one problem with this vehicle. 1) it starts honking while driving, instrument panel and interior lights flash on and off, the car will only make right turns and will not restart when vehicle is turned off. Yesterday, it did it once again immediately as I turned right onto the city street from a parking lot. Luckily there was another parking lot entrance on the right, so I pulled in, parked and turned off the vehicle. It continued to honk, flash interior lights and instrument panel and ignition would not work nor crank. I tried to restart the vehicle several times over a five (5) minutes, when it finally restarted and I was able to get the vehicle home without it happening again. This vehicle has done this several times and it will start honking in the middle of the night while parked and off for no reason. There are times that as quickly as it started honking it will stop, other times, I must go attempt to turn vehicle on and eventually ignition will crank and engine will start. I have taken it to Mazda but they are not able to replicate the problem and tell me there's nothing they can do. I am worried I will not be able to turn one of these days and hit someone and get hit by someone else when the car decides it won't turn left. Not to mention if the car will not start while I am in a bad area and be harmed while waiting for the car to stop honking, flashing and refusing to crank and start. 2) when you put gear in drive, from either park or reverse, and take your foot off the brake the car accelerates and lunges forward without pressing the gas peddle. The first time it did it I almost hit a parked car! thankful I acted quickly and reapplied the brake. Now I allow enough space, as if I driving a truck and am ready to apply the brake. Dealership states nothing is wrong with it. Mazda needs to take these matters seriously. But it's going back!!.