Regarding the effort of "establishing diplomatic relations", I think we might be misinterpreting the "we" in who is actually going to achieve it. Fox is just part of a big mean machine, and so is Kirk: if they all perish trying to broach the Code 7-10 secrecy, then so be it, as this will still have helped a little bit in finding the relevant facts. There would be other ships to follow, and follow soon, unlike in certain other adventures where the heroes stumble onto a danger Starfleet knows nothing of.
Fact-finding is clearly in order, as Spock tells the audience that basically nothing is known of the planet(s). Other parts of the expository dialogue establish that there are limits to what Kirk can do diplomatically, yet basically none to what an Ambassador can (a sensible setup, as soldiers should never have power over gunboat diplomacy!) so having Fox aboard is a good precaution even for a purely pathfinding mission.
Fox can be seen as a selfless individual, as an alternative to him being an idiot. The ship is being fired upon? Scotty and friends can't figure out why - Kirk is stuck on the planet without a communicator. So the fact-finding mission is a total failure. But if Fox beams down, armed with a smile and the "It must be a misunderstanding" pretense, there's at least some chance of finding out relevant facts before Scotty has to withdraw or start acting on his own. Even if that's likely to cost Fox his life.
That Fox subsequently is amazed that he is going to be killed is understandable, really. There would be little to wonder about being gunned down at first sight, and he might be prepared for that. But these people all of a sudden, and very politely to boot, tell Fox that there's a war going on and there's going to be an execution, two rather nonsensical claims that the audience is well prepared for but Fox truly cannot be.
I figure that the Talosians were able to reach Kirk clear out on Starbase Eleven because they had been in telepathic contact with Spock and were using his mind as a relay point.
The other option is that they got their inside man smuggled from Talos to SB11 somehow. They could make the
Enterprise and perhaps the
Columbia crash and burn; with this bit of practice, they might have hijacked the third vessel they lured in, and inserted their operative using that ship.
(If it were a human ship, the easiest sort to lure in with their knowledge of human distress calls and whatnot, its crew would be useless to them - no matter what their goals, stated or hidden, they
were unable to use Pike's crew originally. But Pike is a special kind of human, thanks to his experiences, and they could work with him, warranting the operative-insertion complexity.)
Personally, I feel the maximum range of their telepathy was that which allowed them to create the false distress call in "The Cage" and transmit the imagery in "The Menagerie". And that was too little to reach any starbases or regular shipping lanes, and only worked on exploration vessels headed for Talos, or starships taking shortcuts to get their wounded to a place of treatment.
Timo Saloniemi