Hello,
Welcome to the forum.
For your first question, the best way to do this in my opinion is to take another testube and put a cloth on it so it's dark. Take the cotton out of the other test tube so they are connected. Shine a bright light on the queen with eggs/workers. After some time they will move out to the other test tube (Note: Make sure to leave a small gap when connecting them so air gets in).
Considering that you live in Southern England, I would say the garage is a fine place to hibernate your ants. I go to Devon a lot so I am quite familiar with the capabilities there.
You do not need to create an outworld yet. As the colony is still small if you have workers, you can feed them via the test tube and they will do just fine. What I would recommend when they get to about 20 workers or they start trying to escape when you remove the cotton when feeding them is to buy a disposable plastic carton at the grocery store and put a barrier around the top part.Then just place the test tube inside and remove the cotton. And Wa La, you have an outworld as well as a formicarium.
Ants can survive different periods of time depending on the species. For Lasius, they can go about 5 days without food. What I recommend is to take another test tube and fill it with sugar water and put a carton on it which supplies the ants with a regular source of sugar. They should be able to survive a good week or more like this. However, once every week or as long as they accept protein you should make it available for them.
I would not recommend adding multiple queens to connect to the same outworld as they could end up raiding each other's nests.
They should be fine while traveling once in a while. But make sure not to do it regularly. Maybe once every 6 months. But I would not recommend it.
I hope this was at the least partially helpful. If you have any additional questions feel free to message me/pm me. I would be happy to answer any additional questions as soon as possible. Have fun. Good luck! Best Regards!
-AntsMaryland