Colpitts oscillator not oscillating
My answer:

1.) I do not know because I didn`t recalculate the circuit. However, it is YOUR task to find a suitable design (not using random parts values), see point 2).

2.) At first, you must understand the circuit (why it can oscillate). There is a frequency-selective feedback network with a bandpass characteristic (L in parallel with C1 and C2). Do not overlook that the supply voltage is identical with signal ground. 

Hence, at the midband frequency the phase shift will be zero. A part of this signal (depending on the C1-C2 ratio) is fed back to the emitter establishing the required positive feedback (loop gain).

3.) It is the task of the base capacitor to keep the base at signal ground (transistor in common base configuration and positive gain, see 2).

4.) The classical (normal) output for common base stages is at the collector .