First of all, I'd like to point out that I am aware that this question has been asked countless times and I am aware of the usual solution. However, it doesn't seem to work for me.
When the error
Exception in thread "main" java.lang.UnsupportedClassVersionError: org/telegram/mtproto/state/ConnectionInfo : Unsupported major.minor version 52.0
JAVA_HOME environment variable is irrelevant to how Eclipse will run code, as far as I'm aware. Likewise the compiler settings you've shown for a project don't affect how code is run.
Instead, you need to look at the Run Configuration you're using when you run it, and check the environment there. Make sure you're using Java 8, and all should be well. Click on the triangle next to the Run button, and select "Run Configurations..." to open the dialog with all the settings. Then look at the JRE tab, and ensure you're using the right JRE.