The first section of a typical semiconductor datasheet lists the breakdown values for some of the device's various parameters. As shown further down the sheet, the normal operating parameters have min-typ-max values. How come the breakdown values don't have a range? Surely every device of one type can not have the exact same absolute max values or is there a % tolerance?

If you measured the beta or Vbe of 100 transistors, you'd be hard pressed to find 10 alike. The same must be true of the breakdown values.

Going further down the datasheet, there normally is a large amount of graphical data. Going back to the min-typ-max values listed previously, which values are used to plot this data, min or typ or max?

 

If the datasheet says that the absolute max allowed voltage is a certain value then simply don't use a higher voltage. Use a device with a higher max allowed voltage instead if you use a higher voltage.

The graphs on a datasheet are for a "typical" device which you cannot buy. Most devices are typical but some are worse and some are better. Sometimes all stock is worse (a poor yield) or better (a good yield).