These are all good questions.
1) As far as the specific Hadith from Sulaym’s book and their authenticity, I don’t know off hand. Our scholars have provided many references about which Hadith are authentic and which aren’t. Thus, please consider a deeper research into it.
2) As far as Zubayr’s fate, only Allah knows. We can only act and conclude according to the historical facts presented to us, to me, his actions at Jamal to some degree negated his previous good deeds. Moreover, he was mixed in his actions and it was not clear where his true allegiance lay, much like his son!
3) As far as our Imam crying for him, there is no surprise in this (if true). Imam Hussain (p) wept for those gathered against him in Karbala. I think the message to us is that there were all types of companions to our Imams, some who were hypocrites, some who were weak and some who were the best of the best