It generally depends on the specific circumstances and the local rules for that court, but substantive ex parte communications with the court are usually inappropriate.
It sounds like you are describing motions or stipulations for an extension of time which are electronically filed, and the "Defendant attorney" then serves you a copy because you are not on the Court's electronic filings system (or ECF). Electronic filings are now the norm in federal court, and the court may handle electronic filings more quickly than manual paper filings through the clerk (which may require that the clerk scan a copy for the court's electronic docket). You should also review the local rules because some courts require that you email a copy of the proposed order (in Word or WordPerfect) to the judge.
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Federal litigation is not for do-it-yourselfers. Lots of lawyers avoid it because the procedures are exacting and sometimes confusing to those who do not regularly practice there. I assume you are pro se and the other side has a lawyer. Therefore you will almost certainly lose your case. That said, Federal courts have an electronic filing system and the parties handle many procedural matters such as adjournments and discovery issues by letter which is usually electronically filed, or by email. There are Federal rules that apply in all Federal courts, each Federal district has its own rules and some of the judges have individual rules, too. One of the things lawyers need to do when assigned to a Federal judge is to become thoroughly familiar with the judge's rules. Failure to comply with the rules can have unpleasant consequences. The judges are usually more lenient of pro se litigants in terms of compliance with the rules, but not always.
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Is the attorney actually emailing the judge, which would seem peculiar, or using the court's electronic filing system, which is not only permitted but in most cases required? I am guessing that it is the second.
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