Reverse recovery parameters
\$( I_F/dt)_{OFF}\$ is said to be "imposed by the circuit". What determines this \$I_F/dt\$?  Is it the speed of the switch that turns
  off the forward current \$I_0\$, which cannot be instant?
  


\$( I_F/dt)\$ is determined by whatever components are in series with the diode. If there are no components in series, then parasitic inductance and resistance of traces or wires would determine the rate that the current switches off. Nothing happens instantaneously because of parasitic inductance of materials (and then the speed of light). Because \$( I_F/dt)\$ changes from circuit to circuit it changes how fast the diode switches off.


  
  Although the meaning of words fall out of the scope of this site, you understand the context of the sentence and therefore I
  kindly ask to help me understand, page 4 on AN5028:
  The recovery charges \$Q_{rr}\$, the recovery current \$I_{RM}\$ and the recovery time \$t_{rr}\$, are intrinsic parameters of the
  diode during its turn-off phase. They depend on:
  
  
  \$I_F\$: Forward current flowing through the diode before it turns off  
  \$dI_F/dt\$ : Slope applied to the diode and imposed by the circuit  
  \$T_j\$: Operating junction temperature of the diode  
  \$V_R\$: Reverse voltage applied across the diode
  &nbsp;
  My understanding is that an intrinsic property is an property of
  something in itself, so independent. Can someone please
  clarify?
  
  


It means that if you want to calculate the turn off time, you need to know the forward current, the rate of current through the part, the temperature and reverse voltage. A hint: If there are this many parameters, find the max or min for each parameter and then see if the turn off time is acceptable.

An easier way to calculate the turn off time is to find the S factor parameter to derate temperature (if 125C sounds good then don't worry about it), find the max rate of current through the part (which is determined by your circuit) and then look it up on the graph, then find the turn off time:




  
  I recall I read somewhere the circuit can limit the reverse current, such it cannot 'reach' \$I_{RM}\$
  


I have not read anything that would indicate the reverse current is limited by the circuit. \$I_{RM}\$ changes with the rate the current through the diode as shown in the graph below. The things that most affect

Source: http://www.st.com/content/ccc/resource/technical/document/datasheet/08/e2/48/3e/ae/13/48/cb/CD00002378.pdf/files/CD00002378.pdf/jcr:content/translations/en.CD00002378.pdf