Is теряет strictly in the sense of losing an item? Or can it also mean losing a game?
Nope, теряет could be used for losing items, persons (when he/she dies) or wasting time, but not for losing a game.
What's the difference in pronunciation between ет and яет? Теряет sounds like терет.
I think that's because it's being pronounced fast. Just like "kind of" often becomes "kinda" in spoken English.
Couldn’t this also be translated as ‘My friend often loses his book’? Isn’t свои intended?
Is there an expression in Russian similar to "forever losing" - as in "My friend is forever losing books"? Is that closer to "always" than it is to "often"?