Helen
I am afraid there is too much variation in the system for us to give you anything close to an accurate idea, at one extreme claims are taking only a few weeks and at the other as long as nine or ten months if not longer.
I believe that the DWP will acknowledge receipt of the PIP2 form.
The biggest delay is in the assessment process, it could be weeks or many months.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems