I reckon your brake fluid is low, when you turn a corner the fluid slops over to one side and sets off the low fluid beep/light. Even the slightest moment of low fluid detection will cause 3 beeps but the light only seems to illuminate for the actual moment that the fluid is low enough to trigger the warning. this is why when the fluid is only slightly low you get 3 beeps but only a quick flicker of the light. If the fluid gets lower still the light will probably come on for long enough to spot it.
There is a plastic press in button on top of the brake fluid reservoir, next to the filler cap. if you press this in quite firmly it will trigger the 3 beeps and the red light too.
Your brake pads may be low. skinny pads will make the fluid level drop. If your pads are not low you may have a brake fluid leak.
If you have rear drum brakes the first place to look for a leak is at the rear brake shoe cylinders behind the drums.
3 beeps on startup is another matter. This normally happens to people who turn the key so that the instrument cluster lights up and then wait a few seconds before starting the engine. If you get into the habit of inserting the key and going straight to the starter you won't ever hear the beeps. They reckon that this fault is either the ABS ECU or a faulty low brake fluid level sensor (high resistance) both are quite expensive as the sensor comes as part of the brake master cylinder assembly.