Unless there's something they haven't talked about yet in the show, there's not a reason for Baelish to kill off Robin Arryn.
Baelish is now the Lord Protector of the Vale until Robin comes of age, so he's in control for the forseeable future.
The assumption is that the north will rally around the Starks when the time comes, so as long as he holds on to Sansa, he'd have control over Winterfell as well.
He has control of 2/7 kingdoms now (Harrenhall, the Eyrie), with eventual plans on the third (Winterfell). He's got to be playing the long game, but I can't see what he would go for after Winterfell, maybe Riverrun?
Harrenhal is not one of the seven kingdoms. The kingdoms, and their seats, are as follows: The North, Winterfell; The Iron Islands, Pyke; The Riverlands (Harrenhal is located here), Riverrun; The Vale, the Eyrie; The Westerlands, Casterly Rock; The Reach, Highgarden; The Stormlands, Storm's End.
Dorne was added as the eight kingdom sometime later. The region where King's Landing is locatede is referred to as the Crownlands.
Actually, Dorne is one of the seven kingdoms. The Iron Islands combined with the Riverlands as "The Kingdom of the Isles and Rivers" when the Iron Borne conquered the Riverlands before the Targaryens showed up and took over. So the Seven Kingdoms weren't the Seven Kingdoms until Dorne was brought into the realm with the marriage between the Martells and Targaryens brought it in diplomatically.
Dorne maybe included as one of the seven kingdoms, but the Targaryen conquest split The Kingdom of the Isles and Rivers into two distinct kingdoms. Dorne was added as the eighth two centuries later.
When Aegon used dragons to conquer the seven individually ruled kingdoms that existed on the mainland and forged a huge, strong empire. The Kingdoms were: The Kingdom of the North, the Kingdom of Mountain and Vale, the Kingdom of the Isles and Rivers, Kingdom of the Rock, Kingdom of the Reach, Kingdom of the Stormlands and Dorne.
Aegon managed to conquer only six of the seven kingdoms, consolidating them under the rule of House Targaryen and the Iron Throne. Dorne was joined to the realm only two centuries later through diplomatic means, after a few hurdles on the way, thus making the name somewhat inaccurate.
There are 9 "administrative regions" of which the Iron Islands are one ... They are not alone one of the "seven kingdoms".
http://awoiaf.westeros.org/index.php/Seven_Kingdoms
