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It might not oscillate - the oscillator circuits are designed with those two capacitors as part of the circuit - it 'may' work just on stray capacitance, but it might not be reliable.
Depends what you mean by an 'analogue oscillator'?, the clock oscillator is basically a squarewave oscillator using logic gates, what I would call an 'analogue oscillator' would usually output a sine wave.
Positive feedback is what makes an oscillator oscillate, essentially it increases the gain until it oscillates. If you have just enough gain it will gently swing from high to low, giving a sinewave - if you have lots too much gain it will slam from power rail to power rail, giving a squarewave output.
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