Q: battery cycle count limit

Nothing sudden. As a lithium battery is used more and more it gradually reduces the amount of a charge it can hold. This means that eventually you will find yourself having to charge it more often, so a point will come at which it's not practical to go on - this will depend on your own usage. At that point it will need replacing.

As a very rough rule of thumb, the battery should survive 500 full charges, though in practice you should never fully discharge it: if you always charge it when it is half full then you can do that 1,000 times and so on. However as I say it won't suddenly die.

Possibly nothing as it is an approximation of how many cycles the battery is likely to be useful. Not the following quotation from Mac notebooks: Determining battery cycle count - Apple Support

You can use your battery after it reaches its maximum cycle count, but you may notice a reduction in your battery life. Knowing how many charge cycles are on your battery and how many are left can help you determine when a battery replacement is required. For optimal performance, replace your battery when you reach the maximum cycle count.