The 74374 is a transparent latch which holds the output data from the counters. The bus enable port controls the three state drivers on the outputs. When it is low the the outputs are high or low according to their contents. When it is high the outputs are in a high impedance condition and do not source or sink current. Multiple tri-state outputs can be connected together as long as only one at a time is enabled.
That Forrest Mimms sure is a bright guy -- isn't he?
Like any A2D it takes a DC voltage at the input, and converts it to a digital representation of that voltage. Presumablt it's got a 5V range?, so zero volts will give b'00000000' and 5V will give b'11111111' outputs.
It's a very crude project though, it would be a lot simpler to do it in other ways.
That's not a reason, if you want to do that design you require that specific chip. To move to a different chip requires a completely different design, and we need to know what you want to do with it.