1. I doubt your "sister" has eval. That would make this impractical to do, and it also means he would not be able to do it by console.
2. Wrong font color. There are no public server mods that turn the ban message green. Therefore, it's fake.
3. MrLol can be trusted more than you can.
4. MrLol usually capitalizes his chat, and doesn't say "plz". The log you posted shows that he did not ever capitalize, and he did use "plz".