Regarding the OP:
Are the people in our dreams capable of independent thought?
The 'obvious' answer is no. The people in our dreams are manifestations of the process of the mind. They are psychological and/or neurological phenomena. Even insights and intuitions, which may well manifest to the conscious mind as realisations or knowings, rise from the subconscious mind ... indeed most of what we consider 'conscious' activity is actually triggered in the unconscious before we are conscious of what we are doing ... so the better answer is, I suppose, we do not know our own minds enough to make such determinations, or jump to certain conclusions.
As a trad, of course, I would argue otherwise, with reservations, as the various spiritisms of the last century has spawned a whole lot of nonsense, but I have not closed the doors of the mind to 'magical realism' and the realms of the psyche.
But 'independent thought' does deserve a note of caution. I tend to see the kind of thing as a message from one mind to another, pre-recorded, as it were. Something left in your inbox. A bit like a ghost in real-time. There's a huge difference between a ghost, which is psychic residue and incapable of 'independent thought' – it's not a conscious entity – and a spirit which, if of a certain degree, is capable of intellectual independence and with whom one could dialogue. Not someone to be entertained lightly.
If there is dialogue – and not simply your subconscious putting words into the visitor's mouth – then you're into a quite different state of affairs. Assuming that it's not the case that both – the dreamer and the visitor – are asleep, then the visitor would have to be capable of holding a telepathic discussion with someone whilst doing whatever it was they were doing ... quite a feat of 'multi-tasking'! And if the visitor was, what does that tell us?
It also raises the question of invasion and possession – how easy is it for an entity to enter one's dreams?
If we accept the answer to the question as 'yes', then a number of less-than-comfortable questions follow, not the least being how could you then be sure that your own thought was 'independent'?
As ever, and as someone famously said: 'Kids ask all the best questions'.