I wouldn’t worry about rough seas, which was my fear before we started cruising in 2013. During our many cruises we have encountered rough seas a few times but these large cruise ships are amazing, they have underwater stabilizers that they stick out on either side of the ship while at sea. When booking your cabin try to get a room low down and central to minimize rolling and pitching.
There are many places to eat on board the QM2 not just the assigned dining rooms, so you can eat alone without being stuck in your room. There are also facilitated but informal groups who get together each day at a fixed time for an hour or so. My wife likes to knit so always hooks up with a group of ladies who knit, sow, crochet or simply chat once a day.
On the QM the activities during the days are very varied. We have even had the Royal Shakespeare company on board and also RADA, doing shortened plays. Ever seen every single death in a Shakespeare play performed in an hour? Hilarious.
I think what I am saying is that you shouldn’t be concerned about traveling alone on the QM or any cruise really, lots of people do, and you can choose to keep to your own company or enjoy talking to others.
ETA
Trains to Scotland will almost certainly be change at London, Kings Cross for direct journeys to Edinburgh and beyond, so you don’t actually see any of London, just the inside of the stations.