Severe Disability Premium queries for ESA

Got a few questions about SDP and ESA. As of today, just found out that my non dependant daughter who lives with me (there's just the 2 of us) has been awarded PIP standard Daily Living from 02/05/2017. I also receive this and nobody receives Carer's Allowance for looking after either of us, it looks like we both now qualify for the SDP with our ESA (we are both in the support group).

Queries I have are:

1) Will DWP automatically add this to both of our ESA claims or do I need to contact them and ask them to do it?

2) Is SDP payable to eligible claimants at ANY stage of their ESA claim or only main phase? i.e. will I get arrears of SDP paid back until 02/05/2017 or only from 16/08/2017 when I was placed in the Support Group?

Sorry about the wording, it's quite hard to explain on screen. Just can't seem to find much info on SDP & ESA online. Basically, want to know if will we both get arrears of SDP paid back to May even though we were both in ESA assesment phase until recently? Or only from the times were we placed in our respective groups?

Many thanks