In our system, to be truly higher dimensional you must transcend lower dimensions by a infinite degree, as in, they are minuscule and meaningless to you.
You might achieve this if you see universes as flat or as fiction, like a dream or something, but it takes a lot of context.
In fiction higher dimensional beings vary from just having time and/or space powers, immensurable speed, just being outside the universe or having good acausality, so is hard to see one that truly sees planes as nothing and so warrants tier 1.
To the mind question, yes, but it would be noted that it is only for their minds, as seen with
BB.