The book of Sulaym ibn Qays is questionable in its authenticity and there is evidence that suggests it has many additions and alterations that came years after his death. That’s not to say it is entirely false, rather it must be considered carefully with other appropriate sources.

As far as Zubayr is concerned, although he fought in battles on the side of Rasulallah (sawa), objected to Saqifa and called for Imam Ali (as) to be the khalifa, he also rose up against the Imam as you describe. When he ran from the battlefield and was killed, scholars ponder why he did not just join the Imam, thus questioning whether he regretted his actions. So, it is unknown, and possibly unlikely that he was forgiven. Whether he is considered an apostate is known to Allah.

As far as praying for his forgiveness, I don’t know. To me, why would we pray for someone who rose up against our Imam, and then, rather than help him, run from the battlefield only to be killed from behind.