Help Understanding BJT "On Characteristics" in Datasheet
I think this means the voltage required to forward bias the BE junction, but I figure this would be a minimum value, not a maximum.


That's correct. They're specifying a maximum to tell you, "you won't have to provide more than 0.8 V to turn the device on".


  Secondly, why does the hFE for the first scenario have a maximum value, but the other two do not (just hyphens)?


Because they don't commit to any maximum limit on that parameter.

Every limit in the datasheet adds test time when manufacturing the part, which adds to the cost. So the fewer parameters that have limits, the lower their cost to produce the part.


  Finally, is V_CE of 5.0 V a good bias point? The design I am basing off of, when simulated with a generic NPN, gives a V_CE of roughly 5V, so this makes me think so.


Given you have a 9 V supply, biasing the collector at ~4.5-5 V (relative to ground) gives you near the maximum dynamic range. So Vce of ~5 V is probably about right.


  I used 800 A/A as it is the average of 400 and 1200.


Before you're done, you should test that your design works with either 400 or 1200. Ideally you'll want to design so that the \$h_{FE}\$ can go to infinity and your circuit will still work.