I note that in the first screen version of The ThingThe Thing, the monster is both intelligent and uncommunicative --— the professor at the base does want to communicate with the alien but it, even to its detriment: it could have assuaged the fears of humans by chatting, displays no interest in communication.
In the remakes, it is a question whether the creature ever actually talks to humans --— infected humans may speak to humans, but it is unclear to me that, even if the infected know that they are "things", they say anything they would not have said if they were still human. When the alien is in its fully monstrous or even partially monstrous form, it definitely does not talk. The guy whose hands are transformed and is eventually torched iirc just moans, perhaps showing some interaction between the still-human mind of the man with the alien cells. He moans because he wants to speak perhaps, but the Thing will no longer allow this.
The entire question of infected humans knowing that they have been infected I do not think is clear. The infected doctor'sbiologist, Blair's, behavior kind of suggests that he is acting in the interests of the alien, but maybe the Thing just infected him and the doctor really thinks that destroying the radio is a good idea. On the other hand, he does make a spaceship from scratch so he knows what he is --— but it is still not clear that when he speaks to humans, it is not the human mind, under the control (like censorship --— perhaps the doctor would want to say, I've been infected, incinerate me, but The Things prevents that --— otherwise the doctor gets to say what the doctor would normally say although this doctor knows he has been infected, so his behavior is sort of the interplay between his human side and alien side.)