What happens when base voltage is higher than the collector voltage in a bipolar NPN transistor?
Does the base voltage has to always be (0.7v) in order for a bipolar NPN transistor to work?

No.  But a silicon small-signal BJT transistor usually has a base to emitter voltage of around 0.6 to 0.7V when it's operating.
(Note that you say &quot;base voltage&quot;, and I'm changing that to base-emitter voltage -- the voltage of the base vs. some arbitrary point in the circuit is meaningless, and the emitter isn't always grounded.  It's the voltage from the base to the emitter that matters).

What happens if the base voltage increases or decreases?

Roughly, the emitter current of a BJT increases exponentially as the base-emitter voltage increases.  More base-emitter voltage -- regardless of the collector voltage -- means more emitter current.

what if the base voltage is more than the collector's one, wouldn't electrons just flow through the base current and completely ignore the collector?

This is where things get fun.  The way that a BJT is constructed, if there are carriers flowing out of the emitter into the base, and if the collector voltage is right, those carriers mostly fly through the base without contributing to the base current.  In an NPN transistor (which is what you appear to be talking about) the carriers are electrons, so they are attracted to positive voltages.  So if the collector voltage is above the base voltage, electrons from the emitter, in around a 50:1 or 100:1 ratio, fly through the base and into the collector.
That ratio is pretty close to a transistor's &quot;beta&quot;, or amplification ratio.
This happens even if the base and collector are at the same voltage (!).  Basically, one way to model a transistor is as the base-emitter diode, which is forward biased in normal operation, and the base-collector diode, which is reverse biased in normal operation, and a magic current source that causes 99% of the emitter current to flow from collector to emitter.
If the collector voltage drops below the base, the transistor will still amplify current -- at this point, the base-collector diode is forward biased, with some current flowing in it, but that action can still be overwhelmed by the &quot;magic current source&quot;.  In fact, this is a useful mode of operation, where in a typical 1970's-era transistor like the 2N3904, you can have a current amplification of 10:1 or so when the collector-emitter voltage is 0.2V.  In new &quot;super-beta&quot; transistors you can get useful amplification with this voltage less than 0.05V.