The third level menu items doesn't appear?

The default Mesopotamia menu currently only support two levels menu items depth, however, the UberMenu plugin is fully compatible with Mesopotamia, it allows you to build amazing menus and also add as many levels as you want.

After importing my website, the images(featured images) appear cropped and not in their original sizes?

There are many things that cause this issue, for example, this maybe means you didn’t activate Mesopotamia theme before importing your website content, however in order to solve this issue, you can use Regenerate Thumbnails plugin.

After activating it navigate to Tools=>Regen. Thumbnails then click on “Regenerate All Thumbnails” button.