I wrote an analysis as to why awarding the penalty (clip: streamable.com/puw10a) was the wrong decision:
https://imgur.com/a/gAzf4ve
While I am happy to agree to disagree on what the 'best' decision is for this incident (my decision is still a penalty and a caution), there is one part of your analysis that I must argue about: a) is incorrect in law, assuming there was indeed contact made (which I believe there was, although I've yet to see a photo or video which 100% proves whether there was or wasn't). Law 12 is very clear - "If an offence involves contact, it is penalised by a direct free kick." If there is contact, you cannot give an IDFK here.
Edit: just thought that that would also make option c) incorrect is law too!