Blinking CEL means that the engine is misfiring often/badly enough that it will overheat the catalytic convertor badly enough to destroy it, which can raise your EGTs enough to damage the turbo/engine if you continue driving. So, for most instances, blinking CEL means you pull over as soon as you safely can and have the car towed. Cat convertors for newer cars are NOT cheap, and if Mazda sees that you drove a long ways with the CEL blinking (which you are specifically told NOT to do) they may or may not honor the warranty on the cat convertor. That would be like expecting Mazda to warranty your engine if you drove it 30k with no oil change.
"Limp mode" is not one specific mode. I think the term comes from electronically controlled transmissions, which will go into "limp mode" if it detects a problem with the pressure/shift solenoids or excessive clutch slippage. It will shut off all the solenoids and usually default to 1 gear (usually 2nd or 3rd) and the highest setting for line pressure. Something that one might describe as "limp mode" would be caused by any fault on our car that could reduce the engine output by quite a bit or cause the engine to run really poorly. Some examples might be the knock sensor, MAF sensor, accel pedal position or throttle position sensors...the car will probably not produce any boost at all without the knock or MAF sensors, and the accel pedal or throttle position sensors will either cause reduced power or nothing above idle depending on how many of the redundant sensors have failed. Basically, "limp mode" is designed to allow you to drive your car safely to the shop for repair if possible without allowing the engine to run into a situation where it may be damaged (i.e. running full boost without a function knock sensor is very dangerous

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