It would be useful if you fill in information about yourself in your profile. It gives others context that helps answer your questions more effectively. For now I'll assume you are a student and this is a homework assignment.
There is no such thing as a "common mode differential amplifier". Most integrated amplifiers are differential, meaning they amplify the difference bewteen two signals. They generally strive for good common mode rejection, which means that the average bias on the two signals doesn't matter, only the difference between them. For example, a ideal amplifier (infinite common mode rejection) would see the input signal as being 1mV whether the two inputs were at 1.001 and 1.000 volts, or 5.432 and 5.431 volts.
As for where the signal comes from, that's impossible to say since there are so many many different applications these amplifiers can be used in. It could be from a thermocouple, a high side current sense, a microphone, the detector in a radio receiver, and many many more.
Your second question sounds like something the instructor went over in class and wants you to rephrase back to him. I don't know what he thinks the three methods are, and I don't want to do your homework for you anyway. You need to learn this stuff for yourself. However, there is one property of a bipolar transistor you should keep in mind since it may be useful here. Take a look at a standard set of curves for a typical transistor, or measure them yourself. These have the C-E voltage on the X axis, the collector current on the Y axis, and a set of lines each for a different base current. Such a graph is often referred to as a set of "collector curves".
Once you get into the main operating region, note how each curve is relatively flat and horizontal. This means the collector current is about the same over a wide range of collector voltage. Put another way, the transistor looks like a fixed current sink (NPN) or source (PNP) at that base current, with it being insensitive to the collector voltage. This is a useful property when making a diff amp.
