Bob
I'm not sure what forms you are referring to but there is most certainly a UC50 which is the UC equivalent of the ESA50, the assessment criteria are exactly the same, you seem to refer to this form in your post.
If you are receiving UC payments then as far as I am aware you cannot now go back to an ESA claim. I'm afraid you cannot claim the ESA Assessment rate while you wait for an appeal as this is only payable as part of an ESA claim, as far as UC is concerned, your appeal does not exist.
Yes, you should be completing the Capability for Work Questionnaire, failing to do so will at the very least delay your being moved out of the work group.,
Whilst you remain in the Work group you must participate or you risk your UC payments being sanctioned.
There must be a JC+ advisor who has responsibility for you, it will be the person who is setting the work activities.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems