We know that it's possible to encode and transmit information from sender to receiver using electromagnetic energy. Radio waves do this every day and are the basis of everything from CB radios and walkie-talkies to mobile phones, so we know that it's physically possible and in fact we've been doing it for over a hundred years.
The human brain (or really any electrochemical brain which operates on similar biological principles to the human brain) generates an electrical field which can be detected by a device such as an electroencephalogram (EEG), which is normally used in a medical setting to determine if an unconscious person still has brain activity and more generally to measure the state of someone's consciousness (awake, asleep, dreaming, tired, alert, etc).
Extrapolating from this, it might be possible for creatures to evolve a capacity to communicate directly by sensing the electrical field generated by another individual's brain, or perhaps the brains of nearby individuals, perhaps by having specialised sensory organs in a similar way to magnetoreception in birds (which allows birds to detect and navigate by the Earth's magnetic field).
This might allow one individual to sense fear, surprise, pleasure or curiosity in a nearby individual that they cannot actually see or hear, and perhaps to even form basic mental images of the event which provoked the emotion and it's location, such as a nearby predator, a food source or potential mate.
This would certainly have some interesting effects on the social development of the species. Whether it would be possible to communicate "dinner at Susan's at 8pm, bring the canapes and this time don't get drunk" is another matter.
The quantum brain
The very latest research suggest that the brain (or at least individual brain cells) are capable of sustaining a quantum state, and that this is in effect essential to consciousness. This has some very interesting implications for the nature of individuality, awareness and faster-than-light communication. However, this becomes quite speculative from here, so I'll leave it to your own investigation.
Moving physical objects with thought alone seems unlikely. I'm going to rule out nanobots and other such things as that seems to be outside the scope of the question, though it would obviously make it easier.
Moving an object requires energy to overcome its inertia, friction, gravity and any other forces that might be applied to it. Normally that energy is imparted through physical force applied directly to the object in excess of the existing forces to move it in the direction you want.
So, the question becomes, where would that energy come from and how could it be directed in a moving objects with thought alone scenario?
If you're willing to stretch science a bit and go with thought controlled nanobots (or magic little creatures) or something similar, then you can start to work around these problems.