Circuit analysis / understanding the control board for a heater
What does U1:B do here?


We only have your schematic so my answer is based on this. U1B is operating as a voltage comparator and C4 isn't negative feedback in the traditional way; it's just there to possibly stop U1B's output changing too rapidly. This could be thought of as de-glitching the output of U1B. ZD2 will have some compliance in that if U1B's output goes high, C4 will slightly increase the voltage across ZD2 and this gives a little bit of AC negative feedback to slow down U1B's output.

Bottom line - if the AC current passing through "RMESS" is above a certain limit, it will flash the green LED. I would urge you to get a free simulator and use it.


  I have no clue what R9 and R7 does. Are these some kind of noise
  filters?


If I knew what connected to pin 2 I might be able to say why R9 was present. However, if R9 is needed then, to balance op-amp input bias currents you would add R7.