det does not refer to the keys, it is an empty word referring to 'the thing I am talking about' and it does not change for gender or number. We usually compare it to 'it' in 'It is raining'.
Apart from what I just wrote in answer to kathryn.ne, dem är mina nycklar is actually even worse. dem is an object form and can never be used as a subject in a sentence at all. (since de and dem are pronounced the same way, many Swedes struggle with this, so it is a pretty frequently made error, but it's still considered wrong).
We normally don't say the t in det in everyday speech.
There's a clear difference between the /i/ sound and the /y/ sound, but the /y/ sound is usually hard for learners to pick up, so just keep listening and you'll hear the difference eventually.
I typed in "These are my keys", only to be told it has to be "Those are my keys."
Quite right. det can mean 'it' or 'that' – and in sentences like this, where you don't say 'It's my keys' in English – 'they' or 'those'. For 'these are my keys', we would have said det här or detta.