I am pretty sure it *is* their country house because of the conversation Lisa has about it before she first goes there. You also see them in their NYC home when he orders Zabars, and I think there is one exterior shot of Sam walking up to her door in NYC.

I assumed the same thing about the leukemia when Mycroft said he was already dead - did he ever affirmatively state that Sherlock was right re: the NSA, or just let Sherlock talk? - and I think the hug and "I love you" confirmed it.