Many signs point to Feedburner closing soon as it's not being actively maintained anymore. Although it hasn't closed yet, users have complained about delays in email deliveries, and also loss of subscribers.
Therefore it might be wise to switch now.
Yes, you're looking for a Feedburner alternative, however if you are really looking for only free solutions then maybe you should consider sticking with Feedburner for now, and it covers both the email- as well as the RSS parts.
If you don’t receive the email in the next 2 minutes please check your junk folder, and add [email protected] to your safe sender list.