(1) You have been placed in the ESA work-related activity group.
(2) Your contribution-based ESA is the same amount as your previous payments of IB, because under the transitional payments protection rules claimants will not lose out financially when migrated from IB to ESA.
(3) It is not clear from your post what you mean by "limited work"? Are you wanting to undertake permitted work, or are you merely referring to limited capability for work?
(4) Work-focused related health assessments (WFRHA) have currently been suspended, so you will not have to attend for this assessment.
(5) Income-based ESA is replacing Income Support, but as you receive contribution-based ESA which does not appear to the topped up by ESA(IB) this will represent your full payment.
(6) While you are in receipt of the work-related component of ESA you can be compelled to attend work-focused interviews and carry out work-related activity, but currently you cannot be mandated to apply for jobs.
Nothing on this board constitutes legal advice - always consult a professional about specific problems