"How impertinent you are to write to me about Tom as if I had not opportunities of hearing from him myself"

sounds like a bit of a tease to me?

I would have thought he would have written to Mr and Mrs Austen and not directly to JA.Even Edmund in MP has not written to Fanny , whom at the time he saw as a sister, if you will,while he had been away from Mansfield ,at school:

She had all the heroism of principle, and was determined to do her duty; but having also many of the feelings of youth and nature, let her not be much wondered at, if, after making all these good resolutions on the side of self–government, she seized the scrap of paper on which Edmund had begun writing to her, as a treasure beyond all her hopes, and reading with the tenderest emotion these words, “My very dear Fanny, you must do me the favour to accept” locked it up with the chain, as the dearest part of the gift. It was the only thing approaching to a letter which she had ever received from him; she might never receive another; it was impossible that she ever should receive another so perfectly gratifying in the occasion and the style

MP,Chapter 27.

We know that unless one was engaged it was considered improper for people of the opposite sex to correspond: but,even so, perhaps like the Morlands, the Austens decided it was OK.