I would like to know why a non-inverting input op-amp is used and why not an inverting op-amp?
I think what you mean is, why is the op amp configured as a non-inverting amplifier rather than an inverting amplifier. In this instance, I think either configuration could have been used. However, the non-inverting configuration allows a higher input impedance to be achieved, so it is preferred when the input source has a high input impedance.
Why do we need a feedback loop?
To set the gain to the required value. Op amps have a high (and somewhat variable) gain that drops off with increasing frequency, and are intended to be used with negative feedback so as to reduce the gain to the value that you need.
Also why is that the gain is determined by the ratio of the two resistors forming the divider bridge at the output of the OpAmp?
That's a bit complicated to explain here. I suggest you search for articles on op amp theory and/or negative feedback. You could try
http://en.wikipedia.org/wiki/Operational_amplifier_applications but it is not exactly for beginners.
Also what are the specific uses of the capacitors and resistors used?
C1 is a decoupling capacitor, to keep the op amp stable. R5/R6/C5 provide a filtered bias voltage to the microphone (I don't know what type of microphone it is, but presumably it is a type that requires a DC bias). C2 stops this bias voltage feeding through to the op amp. R3/R4 bias the op amp input to half the supply voltage which will be about the middle of its common mode input range. R1/R2 define the gain of the op amp to be 11 and C3 is a DC blocking capacitor to reduce the gain to 1 for DC, thereby ensuring that on average the op amp output is at half the supply voltage as defined by R3/R4.