Nah, Zoroastrian is not influencing three Abrahamic faiths. Just pretty logic that God will send many of His messengers to not only one group and do it since early human civilization. It is because God is Kind and has Rahmat, He will direct human to Heaven and educate human
Of course we know that Islam is the recent and youngest among the big religion, Islam is just reinforcing what has already been there.
When Older religion get corrupted, then God sends newer messengers to teach human kind, it is pretty logic and natural.
Abrahamic Religion has been dominating the Earth and has captured lot of land. It shows it is true religion.
No religion gets corrupted. New ones like to think so to force their version on to followers of the old. By military force, torture, rapine, and industrial scale destruction and bloodshed.
About Zoroastrianism not being directly influencing the three Abrahamic faiths, you need to read more. From non Islamic sources.
Cheers, Doc