Yes, this service is completely free, forever. But, we limit every user to around 9 emails per month - so this service is meant to be used for important stuff like a test, not day to day things like doing your homework.
It might be because you did not verify the reminder, and it expired, or a server error. Also, check your spam inbox, because it might be stored there.
That is because we are using free services - the reputation of them may not be perfect. But, any emails legitimately triggered by your submission on our platform should be safe.