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.
Evidently all three are grammatical:
unbecoming:
- Not in accord with the standards implied by one's character or position:
conduct unbecoming an officer
(AHD)
unbecoming:
- behaviour that is unbecoming is shocking or unsuitable
conduct unbecoming to a teacher
(Longman Dictionary)
They maintain that Irving's conduct was unbecoming of a reputable
historian.
(http://www.oxforddictionaries.com/definition/english/unbecoming)
Best Answer
I agree with Deadrat that a process or action may be facilitated. That is, they may be helped. I also agree that a product cannot be facilitated. "Facilitated" is an ill-defined and pretentious word and probably should not be used here at all. The word you seek is "complemented". "The product is complemented by three tools". Or perhaps "the product contains three tools". Or "the product features three tools".