I ran a check for error in my SPD 2013 and it shows none. However, it does not send out the email. I read in here that someone switched to SPD 2010 workflow format and then it sent out the email. Is that the only solution?
It's kind of known issue in SPD 2013 workflow. Send mail action is not working in 2013 but it works perfect in 2010 version.
To fix this issue in SPD 2013, You can use 'Pause for Duration' action before 'Send email' action and set it for 1 min, after that it will works as per your expectation.