The effects of distance on mentalic ability are not clear. Stor Gendibal, a Second Foundationer, thinks in Foundation's Edge:
It was well known that the mentalic field did not obey the inverse-square law. It did not grow stronger precisely as the square of the extent to which distance between emitter and receiver lessened. It differed in this way from the electromagnetic and the gravitational fields. Still, although mentalic fields varied less with distance than the various physical fields did, it was not altogether insensitive to distance, either. The response of Novi’s mind should show a detectable increase as the warship approached - some increase.
(How was it that no Second Foundationer in five centuries - from Hari Seldon on - had ever thought of working out a mathematical relationship between mentalic intensity and distance? This shrugging off of physics must and would stop, Gendibal silently vowed.)
A little later,
Gendibal narrowed the mentalic field controlled by his mind. It intensified and leaped across the gap between the ships at the speed of light. (The two ships were close enough to make hyperspatial contact - with its inevitable loss of precision - unnecessary.)
This suggests that mentalic abilities are ordinarily limited by light-speed, but can also somehow operate through hyperspace. However, we do not generally see characters reading and manipulating minds at vast distances. Mentalics, including the Mule, often have to travel somewhere in order to act. For example, we see the Mule dampening the morale of planets he is ready to conquer, but he doesn't do that from afar. Preem Palver has to travel in order to combat the Mule, Stor Gendibal also has to be physically present to investigate, and the Second Foundation relies on agents in-place rather than scanning minds from Trantor.
Ordinary human mentalics can communicate superluminally, and can act over large distances. For Gendibal,
- He speaks telepathically with Compor over a distance of "hundreds of parsecs", and Compor is a very weak mentalic. It's not stated whether that applies for other mentalic abilities, or where the other party isn't themselves a willing mentalic.
- He can handle multiple minds at a distance of about half a million kilometres, or a bit more than a light-second.
- He can detect Gaia's mentalic field from a hundred million kilometres. (That's stated to be more due to Gaia's power than his own detection skill.)
He is a strong mentalic but not treated as exceptionally strong by the others, so we can assume other senior Second Foundation members are at a similar level. I do not think we see any human characters altering or reading minds at hyperspatial distances. The second quoted passage above seems to imply that it's possible, but perhaps requiring great power to be able to overcome the loss of precision.
In Foundation and Earth, Daneel laments that he has "an even more rapidly declining ability to test and influence minds at hyperspatial distances", after describing how from Earth's moon he has subtly influenced events as far away as Comporellon. Comporellon is Epsilon Eridani, which is over ten light years from Earth. He is able to do this partly by virtue of his contact with Gaia (which is much further away) and Bliss is continually part of Gaia in her travels. So if you have the combined mentalic power of an entire planet, plus unknown robot-technology, you can do it. (Bliss herself still needed to be present in this case, but I think Daneel's statement implies that he could do it himself with great effort.)
