Got it wrong because the slow-repeat pronunciation made it sound like 'spieler', picking up the various subtleties in spelling can be difficult.
In the summary page for basics 1 lerne is also translated as "training". Is that correct?
As far as I know, no. Lernen means to learn, while tranieren is to train. I've never heard lernen used that way, but I don't know the context of your example.
"I am playing and am learning" is correct? Wow. Why isn't: "I am playing and I am learning" be correct, then?