I'll buy 1, but for 2, they can implicate Sansa just as easily without actually putting the poison in the necklace.
I realize it's a small detail compared to, say, the NW letting a child give Jon the final stab, but it's bothered me for a long time.
I think it's also just to separate themselves from the poisoning by multiple degrees. Littlefinger has an agent give it to Dontos who gives it to Sansa. That way if Sansa is caught and questioned, she would have to flip on Dontos, who would have to flip on Littlefinger's guy, who would have to flip on Littlefinger himself before it got back to anyone important. And this way Olenna is only in danger during the few minutes between snatching the poison off of Sansa and making the kill, rather than having some Tyrell agent hold the poison before the wedding and be at risk that whole time.
On the Stannis thing, it's also important that they couldn't pull men off of the war with Robb to go engage in a long and costly siege on Stannis just to deliver a finishing blow to a guy who is no longer an immediate threat. And by the time things are done with Robb, there's a relatively short period for them to have pulled their guys out of the Riverlands, gotten them onto boats, and sailed to Dragonstone before Stannis left.
The show messes with the chronology a bit in ways this make this all fit a little less well. In the books Stannis heads to the Wall almost immediately after the Red Wedding, as soon as Davos shows him the letter from the Watch, instead of spending a while gathering men and getting bank loans like he does in the show. And in the books, as soon as she's able, Cersei does launch a missions to retake both Dragonstone and Storm's End from the handful of men Stannis has left behind there, and even then both of those turn into long, protracted sieges because they're well-defended castles.