2. According to the given datasheet, in the Electrical Characteristics 
table on page 2, Digital I/O section, you're operating in the undefined 
logic state for this device, or any 5V/ТТL logic device for that matter. 
Any particular reason why?

A low state,  a '0', for the control lines of this device is any voltage 
between 0 to 0.8V, and a high state, a '1', is defined as any voltage 
higher than 2.4V to Vcc. Anything in between
i.e. 0.8V‹ V‹ 2.4V, will be in an undeterminable state.

For reasons why this occurs, read up on totem-pole configurations, and 
TTL and CMOS logic gate topologies in any introductory college/uni text 
on digital logic, e.g. Tocci or Wakerley. (I presume you know how a 
transistor works in switching mode?) This will also explain your first 
query point.

A reference I thoroughly recommend to anyone learning or experimenting 
with analogue or digital electronics, or even professionally, is "The 
Art of Electronics", 2ed, by Paul Horowitz and Winfield Hill, 1989, 
Cambridge Uni Press, aka "The Silver Bible". It's even available in its 
entirety of 1125pp. on the web. Worth every cent if you decide to buy 
it, although some of the later chapters on microprocessors are a bit 
dated, but useful all the same for understanding modern 
microcontrollers.

Peter, if for some reason your control logic voltages are not in the 
specified ranges from wherever they are coming from, you will have to 
think about about converting them, with a level converter, for instance, 
or putting them through a comparator.