A malfunctioning brake light relay switch will cause your 1993 Toyota Corolla brake lights to stay on all the time. The brake light relay switch is located beneath the drivers side dashboard.
Do you mean What does it mean when the brake and battery lights come on in when it is already started? Check your alternator may be its not working well it cause the battery sign comes out.
A rubber burning smell and smoke near your two front tires could be the result of sticking calipers. The brake line could also be the cause of the burning smell.
brake warning light on can mean your handbrake is engaged or that brake fuild is low. Those would be the first two easy things to check. If your brake fluid is low, you will need to keep a close eye on that, as you may have a leak and that can lead to a loss of your brakes.
Shorts that are too tight can cause back pain, and if it is high riding shorts, it can cause fainting. Tingling thigh syndrome is what happens when shorts or pants are too tight around one's thighs and cause them to tingle.
check your brake pads
Usually the main cause of burning is dryness and/or allergies.
The oil capacity for an 06 Corolla is four quarts. Overfilling the oil can cause many mechanical issues and failures.
Heat up the brake pads and cause brake fade.
It causes pulsation or shudder on the brake pedals.
Posible air in the brake line system. The behavior you described is normal operation. The brake cylinder is power assisted by engine vacuum. When the engine is off you don't have vacuum or the power assist. When the engine is started, the pedal will immediately soften up as the vacuum comes online.
While it is possible it is highly unlikely. A burning smell is usually associated with a brake that is overheating. If you suspect either of these things it is important to get the vehicle looked at right away as they could cause you to lose control of the vehicle.