Lisa
I'm afraid the DWP don't normally accept email communication from claimants, although you can ask.
You can make a new claim for ESA but you will only be paid ESA during the Assessment phase if six months have elapsed since your original claim was closed or you can show that you have a new condition or your existing ones have deteriorated so that you would be reasonably certain to receive an award.
If a Decision in your favour is made then you should receive back payments of the ESA Assessment rate.
Nothing on this board constitutes legal advice - always consult a professional about specific problems