Hi KeithW
Q1) correct, if you were claiming HB, if you were receiving CB ESA then no you would stay as you are.
Q2) Correct, even if you were claiming HB, it's classed as a change of circumstances.
Q3) you are correct, the SDP block was lifted on 27 January 2021 and, instead, a top-up payment called an 'SDP transitional element' has been added to UC for SDP claimants who move to UC. This exta element is only available to those who were entitled to an award of Income support, income-based Jobseeker's Allowance or income-related Employment and Support allowance that included an SDP, not those who only had an SDP in their Housing Benefit.
This is a complicated area so please seek specialist advice if you are in this situation.
Gary
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
