Electrical – Log plot with 5 divisions

If you are using the transistor as a saturated switch then you decide what Ic/Ib should be.

The saturated characteristics of the transistor are guaranteed at Ic/Ib = 10. Most often you'll use a bit less drive, maybe Ic/Ib = 20 unless you are very close to the limits of the transistor.

hFE is gain in an unsaturated condition (as an amplifier) with a relatively huge Vce (2V in this case). It is a poorly controlled parameter and varies a lot from part-to-part and with temperature.

You can say that you should have forced \$\beta\$ << hFE (specified at a high Vce) if you want consistent results.

Plots are only an indication of typical behavior, you need to look at the guaranteed limits for design. The plots may help you interpret the guaranteed results at intermediate operating conditions.

So, suppose you want to switch 100mA. hFE (Vce = 2V) is typically around 100, and does not tail off much as you go higher to 200mA (Figure 2) so we can be fairly sure it doesn't do anything weird, but the 100 is only typical. We can see that hFE is guaranteed to be 40 at room temperature and 150mA, so it should be at least 40 at room temperature and 100mA. It might drop 30% at low temperature, so we're left with a guarantee of 28 at low temperature and for a low gain unit. I think I would use Ic/Ib = 10 in this case, not 20.

Now that does not mean that you can't pull a random BC635 transistor off the shelf and use Ic/Ib = 50 and have it work most of the time, but that is not proper design. Don't be that guy.

Vcc typical 5V (with a minimum and maximum of 2V and 7V) ... why use Vcc = 2, 4.5, and 7 volts as its conditions

Probably because the characteristics at 4.5 V are less desirable than those at 5 V. If they specified values at 5 V, then you couldn't use them with a typical "5 V" supply that could be a little below 5 V. They are specifying the characteristics for a slightly worse case than 5 V so that your supply can have a little slop but you can still rely on those specs.

time the pulse needs to be active ... minimum 16 ns ... typical period 5 ns

There is nothing inconsistent here. The minimum is the real spec. You have to hold the value for 16 ns if you want it to be interpreted correctly all the time. It usually takes only 5 ns, but you can't count on that.