The transformer has very specific fill lines to allow for oil expansion over a range of temperatures. Fill it to the brim and it’s almost certainly going to pop!
Yep. You need that “cushion” of air (actually, Nitrogen under a slight pressure) to allow expansion and contraction. The Nitrogen under very light pressure is used to keep a slight positive pressure on the transformer so as to prevent drawing in moist air when the transformer cools under lighter loads. Moisture = corrosion.
You are correct regarding the fill line.
If I recall, and I was in the relay group so I’m more on the periphery (not the great turner of wrenches), they would refill to the “full” line, and then (at least on larger transformers) circulate the oil through the transformer for a day or so before even energizing it to work out any possible gas bubbles or moisture within. It’s a process, but you don’t just plop it down on the pad, hook up the wires, and fire it up.