I am so sorry that you are going through this and feeling that you have had no support from your lawyer.
With regard to your H's e-mails, is your H represented by a lawyer? If he isn't, in my jurisdiction it would be considered neglect of duty NOT to read your H's letters. If he is represented, she should be sending the letters back to his lawyer and have his lawyer tell him that to contact your lawyer directly is not appropriate. I can't comment on whether or not your lawyer is charging appropriately but she cannot ignore the correspondence, especially if H does not have a lawyer of his own. She is not required to respond.
Perhaps when (if) you decide to retain a new lawyer, given that your H is sending copious letters, you can negotiate that unless the letters affect one of the separation/divorce issues, that you will not be charged.
I hope you find someone that you are more comfortable with who can finalize the things that need to be done.
