Who can make changes to the Electrical Load Analysis (ELA) and what approvals does it require? What process/approval should be followed to verify that ALS is correct and adequately controlled?

Electric load analysis (ELA) is provided by the aircraft manufacturer to the operator.
These data are part of the ICAs (see AMC to Appendix H, H25.5 Instructions for continuing airworthiness applicable to point 5 of the EWIS). Changes to ICAs are changes to the type certificate that must be approved in accordance with Part 21.
Where relevant, a change or modification should contain a difference sheet for ELA, so that the operator can update the current ELA.
CAMO is responsible for the condition of the ELA, which must be in accordance with the design of the aircraft, including its approved changes.
The aircraft owner should have access to all relevant information to fulfil its continuing airworthiness obligations under Regulation (EU) 1321/2014, for example to provide that information to the competent authority on request or to transfer the continuing airworthiness records of the aircraft to a new owner when the aircraft changes ownership or in similar circumstances.
The new CAMO, which receives the aircraft, will verify this data when developing the aircraft maintenance program (see M.A.302).