An harmonic oscillator with RL and RC sections

Given is the circuit below; this circuit is intended to be an harmonic oscillator.

The voltage gain of the voltage buffer at the left hand side of the schematic is a real valued factor $A_{v}$ ; this value can be positive or negative. The voltage gain of the other voltage buffers is 1; for all voltage buffers $r_{in} \to \infty Ω$ and $r_{out} = 0 Ω$ .
The value of all resistors is the same (R), the capacitors have identical values (C), and all inductors have identical values (L) - this is to simplify your derivations.

pict

(a): Which condition(s) must be satisfied to get harmonic oscillation?
(b): Derive the voltage transfer for each of the 4 stages in the figure. Combined these form the loop gain.
(c): Assume — only for this specific question — that $R = 1 Ω$ , $L = 1 H$ , $C = 1 F$ and $A_{v} = 1$ . Draw a Bode plot (magnitude and phase) of the loopgain.
(d): Estimate from the Bode plot, and for the special case that $R = 1 Ω$ , $L = 1 H$ and $C = 1 F$ whether the circuit can or cannot be used to implement an harmonic oscillator when $A_{v}$ can be chosen freely.
(e): Determine whether the given circuit can function as harmonic oscillator for a specific (real) value of $A_{buf}$ . If your answer shows that harmonic oscillation can be possible, go to question (d). Otherwise go to question (e).
(f): IF harmonic oscillation possible at question (c): derive an equation for the oscillation frequency AND (after that) derive an equation for the required value of $A_{buf}$ . Both these equations should be functions of the various component values in the schematic — they may be ugly equations. After finishing (d) skip (e).
(g): IF no harmonic oscillation possible at question (c): swap a resistor and the reactive component in one of the stages in such a way that harmonic oscillation can be achieved, and then redo questions (c) and (d). IF there is no way to get the circuit to oscillate harmonically: prove that!