In "The First Pitch Insufficiency", Amy is allergic to avocados. Now, Sheldon wants to take the avocado plant with them to the new apartment because plants are good housewarming gifts.
As Stuart asks to move in with Howard and Bernadette, there is no discussion between them of him moving out less than 9 months prior. He stayed in the house for more than two years while taking care of Howard's mother, and staying on after Debbie's passing.
Since the WiFi router would physically be in the apartment Leonard and Penny are staying in, Leonard could simply reset it, and change the password locking Sheldon out.