I wouldn't call Jane an adulteress. She had no husband living, therefore she couldn't commit adultry. Even if she had intimate relations with Lord Grantham, which they stopped short of, he would be the adulterer, not Jane. (This is my opinion, not necessarily the legal situation of 1910s UK.)
Lord Grantham had almost as many people around to talk to as he did before the war. Yes, Matthew was sent to war, but Cora, all three daughters, Bates, all the people from the part of his regiment that remained in England, were all there.