Hi, In my experience as an American English speaker, there is no single word to describe this in general. If the context is specifically periods between work in a workday, I’d use “break”. “I have a break between lessons/meetings from 10 to 10:30.” “My lunch break is from noon to 1 pm.” If I am going to have time at a station or airport before some trip, I would say, “I’ll have thirty minutes before the flight/the train”. “Down time” exists in US English, but I personally never hear it used for *short* periods between other activities.

Sparetime

Yes, we call that "down time" (in Canada anyway). An example... "wow you're really busy with your kids and work and your house and everything else, do you ever have any down time? Yes, I get up early in the morning before anyone else, that's my down time"

I arrived at the station thirty minutes early, so to kill time, I bought a magazine and sat down to do the puzzles in it.

I don't think of what you describe as "free time" or "down time" or "spare time" or "break" (though those are perfectly good words for different situations). It's just "time" I'll have some time before my flight and will make some calls. I always have time before my train arrives and I use it to meditate. I had some time before boarding my plane and played some solitaire on my phone.