Does this high-bandwidth transimpedance amplifier ring (Multisim)?
First of all, V_rev does nothing, it is connected in series with an ideal current source (which has infinite output impedance) and a capacitor (which does not couple DC), hence it might as well be 0V (or connected to gnd).


  
  Is the presented front-end stable? If not, what part of the Bode plot tells me about the stability? What value do I need to adjust to stabilize the design?
  


Yes it is stable, within the frequency range that you have sweept over.

For an amplifier with transfer function:

$$G(s)=\frac{V_o}{V_i}$$

If we put it in a feedback loop, where the feedback has a transfer function H(s), then the new transfer function with feedback becomes:

$$\frac{G(s)}{1+H(s)G(s)}$$

for an amplifier with feedback loop to be stable means the denumerator of this equation must not equal zero, this happens when:

$$H(s)G(s)=-1$$

This is the point that we are trying to avoid. If we hit this -1 point at any frequency then the whole system is unstable.

How stable your system is depends on how far it stays away from the -1 point, ie. what the minimal distance from the -1 the transfer function is at the frequency where it is closest.


  
  How much of my understanding is correct?
  


What you describe is reasonably well understood.


  
  Is this correct? How would I simulate the noise gain with Multisim?
  


No, to the best of my knowledge, this is not correct.