When we click on Resume Later on a survey, we noticed that email are not always delivered or there is a significant delay unrelated to the email server.
I don't see how Limesurvey would delay the delivery of an email. Either it triggers the sending of the email with the email server or it doesn't.
So you will need to check where this delay comes from or why these emails haven't been sent. Difficult to help with these things, as we do not know your server setup, your email server, etc.
I don't think that you can include another email of an admin for the resume later feature. Also, this would only work with non anonymous surveys as this could breach anonymity.
I don't really use this resume later function (also because people just forget anyway).
If you use token based surveys I would actually switch this feature off completely and use "token/user based response persistence", so respondents can go back to where they have left off by clicking the token link.