RF Downconversion using Heterodyne Principle
after a RF down-conversion using heterodyning principle, will there be an information loss?


No, if the original signal was band-limited, and the bandwidth of your IF processing is sufficiently large to capture that. (so, if you've built a sensible heterodyne receiver.)


  If we translate to a fixed IF frequency, is there is an intuitive way of explain that the information can be retrieved?


Yes. Shifting a frequency is just multiplications with $e^{j\Delta_f t}$, and that's an easily invertible operation (multiply with $e^{-j\Delta_f t}$). 

If an operation is perfectly invertible, no information was lost.


  Is it correct to say that it is the relative change that matters during demodulation? 


I don't understand that sentence, but I think you really mean "what matters is the bandpass content, not the carrier frequency", and that would be right. See: equivalent complex baseband.


  For example for AM it is the amplitude change and for FM its frequency change and this does not change even if we down-convert to a fixed IF frequency?


This depends on how you do the AM and FM demodulation – if they work the same no matter the carrier frequency, then clearly yes.