Has it ever been canonically (or beta canonically) established as to what distance Betazed telepathic abilities can work? I ask as I’m writing a fanfic with a part Betazed original character (Maternal grandmother was Betazed).
Encounter @ Farpoint, as well as a few snippets from season mono*, do say she can read minds but not contact or manipulate them... apart from that one time she telepathically gave a heads-up to Riker... E@F actually showed some proper character potential as, without Troi, they would never have figured out that the station was a giant seafood delicacy with big lasers that can produce buckets full of apples out of thin air. Which sounds silly, but Troi's abilities with non-humanoid life forms SHOULD have been a robust boon to this show, but while I agree not every week can have nonhumanoid and incorporeal aliens, 90% of the time she just parrots "Cap'n, I sense the obvious". Marina got a raw deal, but she did so much with so generic dialogue in ways other actors wouldn't be able to make it work at all. Fortunately she would get the occasional bit (e.g.
The Ensigns of Command revolving around the tea cup and describing it to other species and so on**) that also show a side of Troi they could have used a lot more often because she marvels in those scenes as well.
But, pretty much, she can read minds of most species, from any distance in space, and communicate full duplex with other Betazoids...
...until nigh on a decade later in "Nemesis", where she can, all of a sudden, send all sorts of thoughts to the Viceroy as a newfound convenient plot-resolvin' feature... thankfully "Nemesis" is so much less than the sum of its parts, or else the next movie would have scribbled her out even worse...
/soapbox
* since a lot of people apparently love revisiting season one just as much as they do gettin' mono, but that's not important right now :P
** it's honestly a superlative scene, and more interesting than half the pew-pew Borg Battles IMHO