'the alarm went off'. Apart from that, and your typo of 'natural', they are fine.

Thank you! So , there is no need of using past perfect.

I would say "I set the timer for 10 minutes, and when it expired, the alarm went off." As they are though, "had expired" sounds a little odd, especially for just colloquial speech. You'd also need a comma following "expired," as it's the end of a clause.