Need help : on a short gig (mgr doesn't like me) (tips, jobs)

[Dprofessional]

I am at my beginning of the end of a short gig. I joined in January a company as a perm.
My hiring manager was good and had a good rapport. Things changed rapidly and a new mgr came in.
She thinks she is the queen of "logic" and is quick judgemental.

Long story short, she treats me as dumb-as* and is ready to boot me out. Unfairly put me on a pip plan.

Ok, so I have no choices but to be on the market searching for jobs again

Can someone advice me quickly on

A) is it ok if I leave this job on my résumé ? ( have a company (me and my friends, been working on the side) to backup and prove as needed)
B) any tips on speeding up search when on pip and my days in the current are numbered


Thanks