If you are in the esa support group can you also claim dla/pip and carers allowance?

I have been put in the support group for esa and get £166.80 per week, I do not know what is included in this but it is for me and my husband. We also get £72 per week housing benefit.

Is it possible to claim for dla/pip for me? Which is it now, and how do I claim? Do i automatically get this because of the esa or is it different?

Is it possible for my husband to claim carers allowance and can this be claimed on top of dla and esa? Or is it one or the other?

I am not greedy, the new council tax rules are causing a lot of stress as money is tight. The housing benefit does not cover the rent and i do not need another bill on top.

Thank you