C2 provides the crystal's specified load capacitance and also works as a voltage divider. If You don't understand the circuit
or doubt it's not suitable, use a different one from a text book.
P.S.: I think a crystal oscillator with a high-pass feedback is at risk to fall into overtone oscillations, if the modes are not
well supressed in crystal design. I would prefer an unbuffered CMOS gate as crystal oscillator.
Yes, but don't forget negative feedback.
R3 provides 100% feedback for dc. That's necesssary for opamp biasing.
However, for frequencies in the region of oscillation the negative feedback must not dominate - otherwise the circuit wouldn't oscillate.
Thus, the inverting input has to be ground referenced for these frequencies.
That`the task of C1.
By the way: As C2 is connected in series with the crystal, the crystal operates in its inductance region (series resonance with C2).