Only do this before bottling. From all over the forums, and from high profile homebrew people, it seems that keeping your beer for up to four (or even six weeks) in the fermentation bucket is really no problem.
I sometimes move my fermenting beer to a second vessel, in two cases:
When I want my beer more clear, somehow this helps
When I open ferment, when ...
No, from brewing just with yeast, and even from a bit of freeze distilling, you won't get harmful chemicals in your beer. Also not from letting it stand before you added other yeast. It could get contaminated with other bacteria, yeasts or fungi, but at 7% alcohol at that point, I doubt if they would feel fine and ferment further.
The test with the flame ...
There really is not reason to transfer for just adding a couple vanilla beans. I'd just drop them in and replace the airlock and give it a light swirl to get them moving a bit. You might see some bubbling but its just CO2 escaping.
You may or may not see bubbling in the airlock. With a lot of head space, it may be reduced, and you may not notice it at all. Watching the airlock is like reading tea leaves... could be true, could not be.
The only way to know how fermentation is progressing is to take gravity readings. If the gravity is reasonably close to the expected final gravity and ...
If the end product you are getting is nicely carbonated and you are not getting bottle bombs, and you like it then it sounds like you are doing it right.
I make my ginger beer far more like a fruit wine, but I have friends that follow a method very similar to the one you mentioned and their ginger beers are also very tasty.
If it works stick with it :)
Just be patient, it is perfectly normal for there to be little to no pressure after the first day. Especially if you do not live somewhere hot to supercharge the yeast.
If you do not start seeing any activity by day 3 I'd add another half cup of your now very active ginger bug to get it started.
I live in a hot climate and I need 2 days for second ...
Let me answer your questions
You will need that 2 gallons of head space for foaming. Don't use a six gallon bucket.
Air is less of a concern during primary because of the volumes of CO2 produced but once the active fermentation has stopped, you need to be sealed in a carboy that is topped just a couple of inches from the bung.
You want as little headspace ...