As a new user with eMClient on my laptop, should I be able to download to a mobile and tablet?

Licensing and Downloads

What do you want to download to your tablet and phone?

eMClient itself so that I can access emails when the laptop isn’t available

eM Client is not available for iOS or Android. However, with the IMAP protocol the email you see in eM Client can also be seen in mail apps on Android and iOS because it is stored on your mail provider’s server.