Is a letter from an attorney full of allegations considered a statement under oath?

Short answer: no.  There may be other repercussions for saying false facts verbally or in writing a letter, but "perjury" is not one of them -- and a host of privileges make even outrageously false assertions in connection with litigation usually unactionable.  The details are, well, detailed, and can backfire, so you should consult with knowledgeable counsel before taking any action of any kind.

The perjury allegations will have to go before the court to show there are lies. But allegations are allegations and not necessary truth. You have a right to respond to this letter of course to show what is being stretched. An attorney is an officer of the court but letters are not under perjury or court from what info you provided.