Of course it does. God created man sovereign on earth. You don't think God has an image (face), save for the humanity of Christ.
IF personality is NOT included in that idea, then it means nothing
No, it has nothing do with the personality; it has to do with the dominion.
But He also created man in His likeness, that is capable of mercy, wisdom, moral prudence, so that we can govern this dominion justly and prudently and morally upright, imitating God in His dominion.
The Bible differentiates the image and the likeness. This is obvious in Hebrew as well as in Greek; the "image" being more symbolic represntation [Greek: eikona, an icon], and "likeness"[Gr. homoiosis, similitidue, from the root homoi, similarly].
No, it has nothing do with the personality; it has to do with the dominion.
Oh, so you would say that sharks are created in God's image because they have dominion over the sea? The same for lions in Africa, etc.? :) Yes, man has general dominion over the earth, but many animals have actual dominion over their habitats. This is not the correct distinction between men and animals. God creating man in His image means in part that He created us as personal beings, just like Him, such that we can communicate with God on a meaningful level and we are able to love Him and understand to some extent His love for us.