The spell is badly written.
The first sentence of mind blank is a mix of natural language ("any effect that would sense its emotions or read its thoughts") with a modest amount of game jargon (psychic damage, divination spells, the charmed condition). The result is crisp and clear. There is room for debate around the margins--does X effect count as sensing emotions/reading thoughts? what does immunity to divination spells do if you aren't the direct target of the spell?--but these are corner cases which can and should be left to the individual DM. If it ended here, it would be fine.
But then we get to the second sentence and it all goes to hell. This sentence is phrased as if it were merely clarifying the first (mind blank is powerful enough to trump even a wish). But it then offhandedly introduces a whole new scope for the spell--"affect the target's mind or gain information about the target"--which is neither mentioned nor implied in the first sentence. And it's not clear whether that is deliberately meant to expand the spell's capabilities, or whether it was just a poorly-executed attempt to rephrase the first sentence*.
If we read it strictly and literally (the way you aren't supposed to read natural language), this new scope applies only in the context of wish and similarly powerful effects! So a lowly suggestion spell works on a person under mind blank, but wish used to duplicate suggestion does not. I'm fairly positive that isn't the design intent. But it's what the spell says.
All that said, the effects given in the first sentence are pretty weak for an 8th-level spell. So I would go ahead and apply that new scope from the second sentence, across the board. As for command: While the actions given are physical, command requires that the target can hear you and understand your language. That strongly implies that mind control is involved, and I would allow mind blank to stop it.
*My guess: It started out as an accurate rephrasing of the first sentence, and then somebody changed the first sentence and forgot to adjust the second.