There is no "Recycle Bin" per se but there is an alternative that you can try.
If you start using OneDrive (i.e. picking the option to automatically upload videos/images and so forth to OneDrive), then you can delete files on there which does put files into your OneDrive recycle bin.
Some other points to consider:
You weren't specific about what you want to put into Recycle Bin (you used the work "messages"). If that means e-mail, then there is a trash folder that email goes in to. If you mean text messages, then even OneDrive cannot help.
You said you are using the Lumia 710 which can run Windows Phone 7.8 and nothing further. This means that even if there is an update to Windows Phone 8 that includes something along the lines of what you need, you won't be able to benefit from that.
Edit: tool found to back up text messages
Take a look at this app. Windows Phone has a backup mechanism that is not exposed on any native Windows Phone interface but can be done. This app also allows you to backup texts messages and more to OneDrive which is handy.