Operational Amplifier Feedback
Can any BJT, MosFET, or JFET transistor be an amplifier of any kind? 
Vaguely, yes. However, certain transistors are better at amplifying different types of signals in different ways. 

Are there advantages of BJT being a specific kind of amplifier?
BJT's have a wide linear region compared to MOSFETs, however, JFETs typically have an even wider linear region. Unfortunately, JFETs are typically more expensive compared to a similar BJT. Also JFETs are more difficult to use (negative bias at the gate AND really easy to let the magic smoke out). They also don't typically come in higher currents and voltages. So, BJTs are better at mid and high power analog circuits (even though they have their disadvantages too: lower input impedance, less linear than JFETs, REALLY needs temperature compensation for high power uses, and more..)

Now, considering a basic op amp (voltage difference amplifier), can it be used as any of the four amplifiers (current, voltage, transcondutance, transresistance), how?
Yes, a standard op amp can be made to amplify these four ways. To accomplish this, you don't. You buy an opamp made for the type of amplification you are doing (e.g. a transconductance op amp) because they will work significantly better than modifying a basic op amp. If it's all you have.. google " 'type of amp' op amp circuit" (e.g. "transconductance op amp circuit") and click images. Sorry, I am lazy - this would take forever.

Can be a op amp circuit (inversor, non-inversor, summer, etc.) any of the four amplifiers (current, voltage transcondutance, transresistance)? I'm not sure how this is different from the previous question. One MAJOR disadvantage to op amps is that they usually can only go -15V to +15V and &lt; 100mA max. You can buy power op amps, but they usually aren't very linear and are expensive. At this point you use discrete transistors to bring the voltage up. EX: a 100W stereo typically can swing from (approx) +30 to -30V at 2A. To do this, almost every decent stereo uses discrete transistors in the final stage.

If that's possible, how would they be implemented? same as above.

What i want to know the most is like a yes/no question.Here it is : Can the four amplifiers configurations be made interchangeably from any (one unit ) electronic device ( bjt,jfet,mosfet) or integrated-circuit ( basic op amp and op amp circuits )? With circuits, you can ghetto-rig just about anything with a handful of transistors, resistors, capacitors, inductors and a power supply. If you have a handful of op amps as well, you can make the same circuits but smaller and usually a little better.