Can I just say "your library" instead of its owner's?

I thinkt that is safe; your graveyard should already only contain things that you own.

If you're just after simplifying; why not drop the 'coloured' and 'creature' parts? Or even the djinn trinket-text? Though that does lose flavour.

This should say "on top of your library." Also subtypes are capitalized. Doing so consistently makes it easier to process card text.

Should the activation cost include some mana? At common it helps to create those shields-down moments or go for a straight triggered ability: "When ~ dies, you may put..."

There's an argument to say it should include some mana, yes. But even in its current state this is still incredibly niche and weak. In order to be anything other than a 1/3 for (poor stats), you need 1) to have an artifact of CMC >=4; 2) for that artifact to be in your graveyard; 3) to control a Djinn. And in reward for jumping through those three hoops, you don't even get card parity for giving up your poor-statted 1/3 for : you get card disadvantage saccing it, and the artifact doesn't go back to your hand, only back on top of your library.

So this is currently very unappealing. I'd suggest it should be a 2/2 or cost for a 1/3; and the artifact should come straight back to your hand. In exchange, add a small mana cost to the ability like ", Sacrifice ~:". Or SecretInfiltrator's trigger suggestion is good too.

Maybe it's too narrow? Unless you have many Djinns and many artifacts with CMC >= 4. Even then, it's not that good.