på vejen i think can also mean 'on the way' - en route' to somewhere, not only literally on an actual road
You're right it can mean both. I would try not to use spille when you'd say play. Spille means something more similar to "game/gaming" its an action not just a general behavior.
How can I report excercise I did some time ago? I am asking in case I got similar piece of advice.