I copied a text from MS-Word into BulkMailer. The email looks different and there are problems when editing.

MS Word creates a HTML that is very inappropriate for further processing and for sending by email. Such problems occur not only in conjunction with BulkMailer. Better use a real HTML editor. If you absolutely want to use MS Word to create HTML, you should save the Word document as filtered HTML. Import this file into BulkMailer with menu Email->Load website from file.