Spoilerie Chat Con't
Yeah I had several of the same thoughts bouncing around Bob.
As far as him going alone I think it was briefly stated as protocol for a lone shrink/negotiator to go or that was what 'the company' had managed to secure. This made it the more strange that Clooney's character got to go after his recent loss and obvious mental state of grief which had him vacant at best.
The absence of rescue team was weird but I think they and the 'missing' crew, such that it was, consisted of suicides who were either dead onboard or went off with their new friend

It appeared that although the ship was huge it had a substantive AI element that did the driving/running. The crew appeared quite God-like.
Which crew member's visitor do you mean? The woman's one she offed. The guy's one was never seen until the end when it turned out it was a replica of himself twin-like/narcissus ala shrinks' field day! Then there was the little boy who came back at the end. So which one am I missing? Ooh, was there another dead un, I think there was come to think of it, but didn't they just say his visitor stopped coming. Yes I think they did, which had me considering that the visitors would perhaps 'wear out' without their creator's mental juice. But then the boy was still there at the end, so get the Asprin Matron.
The problem I had was that the fatalistic element was put in play really well and worked but was then destroyed by one of the visitors killing his creator. When it was fatalistic and of emotional draw I thought this to be an excellant tag; as I sat there pondering how, if news of the phenomena broke out on Earth, bereaved people would no doubt flock there en mass. A real shame as the innocuity/un-threatening nature of the visitors made for more mental meanders of wo/man as their own worst enemy to emotion as opposed to the typical threat that 'aliens' of much sci fi represent.
Still, as you note, the questions were left to puzzle and to that extent it worked though perhaps not as well as could of been done - if only a couple of English brains were drawn upon