1. It depends on a season.
During spring (after applying fertilizer) and in early summer your grass will grow quicker.

Later in the summer when it is really hot and wet, the grass may be stressed and will not need to be cut as much.

2. It depeds on the grass.
Bahiagrass, for instance, needs to be cut every 5-7 days during the active season. Otherwise, you will see a lot of seeds come up very quickly. (Best to keep it 3-4" tall)

St Augustine can be cut when it reaches 3 1/2" to 4" (mowing height for St. Augustine is about 2"-3" during wet seasons. Keep higher when it is dry).

Remember: mowing helps promote growth!