Esa

You don't need to do anything until you receive the migration letter. In that letter it will tell you that you need to claim UC by a certain date, which will be within 3 months of the date of the letter.

When you claim UC your ESA will continue for 2 weeks and then stop. Same applies for housing benefit if you receive that.

You will not need to provide a fit note because you're in the work related activity group. This would be Limited capability For work for UC. If your ESA claim started before April 2017 then your UC will include payment for the Limited Capability For Work. (LCW)

PIP continues as normal because it's not part of UC. If you're claiming council tax reduction this will be recalculated based on your UC entitlement.