Starlet
Your PIP award will not be affected by or affect a UC claim, at least at the moment, depending on the award it may increase the amount of UC you are entitled to but this is dependant on changes that are being looked at by the DWP.
Your ESA(CB) will be migrated into UC as well, meaning that you will not be asked to work or to seek work, however, this is a manual process and can take several weeks to be done. Make sure that you tell the UC department that you have an award of ESA as they have no access to this system.
Your ESA(CB) will be treated as income and deducted from your UC, so they will calculate a UC amount based on your ESA award, HB and Tax Credits and then the ESA(CB) will be deducted from this.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems