What preposition should follow "jealousy"?
Q1: Is it jealousy of sth or jealousy at sth or jealousy about sth when referring to the reason why someone is jealous?
I would think you would use the same prepositions for jealousy as for jealous.
Paul was jealous of Bill. Paul expressed jealousy of Bill.
Paul was jealous for/over his wife. Paul expressed jealousy for/over his wife.
Paul was jealous for/over Bill's car. Paul expressed jealous for/over Bill's car.
Somebody correct me if I'm wrong, but I believe you can use either for or over with jealous in either of the latter two senses it holds above.
I have never heard that you could be jealous at something or about something, but if the usages are valid, I would expect that you could use them in the same with jealousy.
Q2: Is it common to say jealousy of sb when referring to the person of whom I'm jealous?
Jealousy of/for/over/at/about something is awkward and in my experience little-used. It is more common to say, "I am jealous of him," as in the example first sentences above.
A search of the COCA gives the most common prepositions following jealousy as: of, in, over, and for. If you sort by relevance, the most common are: among, toward, over, between, and of.
Your could say, I'm jealous of Mia over her beautiful hair/for being able to do a backflip.