I'm sure those more knowledgeable than I will correct me, but I'm pretty sure the cottage is there in 1795 and positive that it's in 1840.
I don't remember seeing the cottage in 1795; it seems to me that anybody who didn't live at Collinwood or the Old House was given a place that had a more period look to it. And in 1840, I believe the set was used, but that the occupants did not live on the Collinwood estate, so that it was not the caretaker's cottage.
But if Matthew were still alive, of course, Roger would have to put up with Laura staying in the Great House itself.
I doubt it. I don't think Laura was ever going to agree to stay at the great house; I think she would have remained at the Collinsport Inn. The Old House is unoccupied, but I doubt she would have been able to persuade Elizabeth and Roger to let her stay there, although I think it would have been sufficient for her needs. After all, Maggie said something the other day that indicated Laura doesn't need food or drink, and Laura apparently never unpacked her bags at the Inn, so the lack of amenities at the Old House wouldn't bother her to much. In fact, I'd be starting to wonder if she actually physically existed when nobody's looking - but that question was answered today, when we saw Laura alone and in private for the first time, at the cottage.
Carolyn was very much Carolyn today - unable to refrain from talking about Burke, and unable to imagine (or so I'm figuring) surviving overnight without a makeup bag.