Some questions on NPN transistor
1) Talking about "base voltage" is indeed confusing and I think it actually means nothing as a voltage is always between two points. If the emitter was grounded then it could make sense as then the "base voltage" could be the potential on the base. But there's no ground in the circuit! So "base voltage" means nothing.

I'm quite sure the writer means \$V_{be}\$ when writing "base voltage". This is because "more electrons flow" when the "base voltage" is increased. It would be better to write:

When \$V_{be}\$ is increased, the voltage across the Base-Emitter PN junction increases causing more current to flow.

The base current is simply the current flowing into the base contact through the \$I_b\$ current meter.

2) Increasing \$V_{be}\$ means more voltage across the Base-Emitter PN junction. That PN junction behaves as a diode. Look up the behavior of a PN diode and remember that the relation is exponential so even a small increase in voltage causes an very large increase in current.

3) The collector just "catches" the electrons that made it through the base (which is most of them since the base is very short) and these electrons from the collector current \$I_c\$.

This is a common base transistor No it is not.

You can use a bipolar transistor (NPN or PNP) in a common base circuit configuration. This relates to using a transistor as a signal amplifier. Other configurations are Common emitter and Common collector.

A transistor is never a common .... transistor. Any transistor can be used in any of the configurations I mentioned. But this is circuit design and not device physics/ how a transistor works, those are really separate subjects. Related though but still separate.