Hi haz
ESA is an indefinite award with scheduled reassessment based on the Prognosis Date completed by the assessor in their report, so your existing ESA award continues in payment until a new Decision is made. We cannot tell you when you are going to be re-assessed as it varies from person to person.
No do not wait to apply for PIP until you have had an ESA assessment. You cannot backdate PIP, PIP starts from the date of your phone call.
benefitsandwork.co.uk/guides-for-claimants/pip Gary