It's certainly theoretically possible to alter mental states at a distance through EM waves. However, leaving aside the problem of evolution (it seems like a massive step requiring a lot of rewiring with no advantages in the intermediate states), it doesn't seem feasible that a humanlike animal could actually produce enough electrical power to transmit the (incredibly precise) waves over a useful distance. That precision is also problematic - you'd have to not only transmit exactly the right 'thought', but you'd have to transmit it to precisely the right place in the brain - no point stimulating the visual cortex with an auditory message, at best that'll just be confusing and at worst it'll have no effect at all.
It's also important to bear in mind that we don't actually have electromagnetic waves bouncing around in our heads - we have sporadically firing neurons. The projected waves wouldn't just have to change the pattern of existing waves, but would face the much harder task of getting particular neurons to fire in particular orders. To illustrate the difference: we already have EM pulses that can interfere with electronics, and it's conceivable that we might be able to build sufficiently precise EM pulse generators that we can, say, rewrite a computer program at a distance, or remote-control an electric car. As it is, the imprecise EM pulses generally just fry all the electronics they hit. But: EM pulses have no effect at all on organic brains. Affecting an electrochemical system at a distance would require an order of magnitude more radiation.
And those waves of radiation have to penetrate deep enough into the brain to trigger neurons not near the surface, while at the same time not simply frying the neurons nearer the surface...
The problems can be seen just by looking at real electroreception. It only works in water, because the waves can't pass through enough air to be in any way useful. [Echidnas can get some signal by having their electroreceptors very close to very damp soil]. Even in water, fish that have evolved to communicate through electric fields only have an effective range of, at most, a couple of meters. And that sort of communication is barely more subtle than "hi, I'm here, I'm a female such-and-such".
It's true that humans have devised ways to effect the brain through EM at a distance. We can make you twitch, and we can unreliably make you see flashes of light. To do this, we need a magnetic field similar in size to an MRI machine's field, and we need to place those magnets right next to your head - and to actually target even a particular area of the brain you need those magnets to cover something like half the length of your skull, because of course the only way to target a particular point with a wave is to have two waves begin a distance apart, so that you can target the focal point.
This has problems, however. In order to have enough power to go from just outside your skull to a couple of centimeters inside your skull and still be able to randomly knock out enough neurons to make you maybe see a flash... well, let's just you mustn't have any metal touching your skin, because that amount of power heats up metal enough to burn skin on contact. [They discovered this the hard way - don't use metalic EEG monitors when you're putting a magnetic field through someone's head!]. And even if you don't have anything metalic on you, you're still likely to get skin and muscle pain, because to get to the brain you have to go through the skin and the muscle.
Leaving aside the question of whether the precision to target individual neurons in specific orders from some distance away is in any way even vaguely feasible, we can get a vague idea of what you'd have to be like to be able to do it, power-wise. You'd have to be eating every minute of the day, preferably eating uranium, and you'd have to have biologically evolved superconductors in your brain. You wouldn't bother with putting pictures into people's heads, because you'd be a walking death ray, except that the chances are you'd fry your own nervous system the first time you tried to transmit. Or just boil your own blood by heating up the iron...
(for comparison, the most powerful bioelectrics in reality are the electric fish, where a big part of their body is based around electrogeneration, and it shapes their entire way of life... the maximum any animal can produce is around 600 volts, or around 1 amp (not in the same animal - high voltage fish have low current and vice versa).)
Incidentally, if you can put a picture in my head, let alone put a thought in my head, you can also control my body. Actually, controlling gross physical behaviour would be a hell of a lot easier than controlling thoughts, or even just controlling sensations.
Fine control of anything also requires the tendentious leap that we all have identical brain layouts. While it's true that most of us have the same brain scheme on the gross level - certain parts of the brain do certain sorts of things - there's no reason to think that the neural layouts themselves are the same for everybody, rather than being functionally equivalent networks that have developed in each brain semi-independently (and the fact that completely different areas of the brain can be rewired for certain purposes when the original wiring elsewhere gets damaged certainly seems to suggest that the detailed architecture is variable, both between people and over time). This would make anything more precise than general stimulation of this sense or that, or maybe this emotion or that, completely impossible. Perhaps, as a stretch, it might be possible over time to learn the layout of one person's brain enough to influence it? But to influence the brain of any random person you haven't met before... completely impossible. Impossible for three reasons: you can't produce that much power, and if you could there would be massive sideeffects; you almost certainly can't target that power sufficiently precisely; and even if you could you wouldn't know where to target it in more than the most general terms, except perhaps after detailed study of the subject.
Passive telepathy, on the other hand, is a lot more possible. It could theoretically be possible to have EM receptors delicate enough to detect the tiny bioelectric changes that accompany thoughts (and to have them be able to cancel out your own bioelectrics, and the magnetic field of the earth and whatnot). You'd still expect only to be able to get very general impressions - telepathy, not telepsychy - though maybe between individuals who knew each other well there could be more, or perhaps the species has evolved to be very similar in this respect. And this passive telepathy could be boosted by the 'sender', who wouldn't so much actually send anything but would think 'really hard' and order their thoughts in a certain easily-read way.
This would be possible, though still very, very unlikely, and hardly worth evolving. But it would be a mere miracle of nature, rather than, in the case of thought control at a distance, an actual honest-to-god miracle.
Needless to say, all this becomes a lot easier if you have physical contact, particularly physical contact designed for telepathy, and if you have penetrative contract straight into the nervous system it becomes almost no problem at all (I say almost because the problem of translation would still exist - the individuals would still have to have evolved specifically for their thoughts to be readable, or else the individuals would have to know each other really well).
What's overwhelmingly easier is ideomotor telepathy. This is the principle that mental states are expressed in body language, and hence observation of the body allows deductions about the mind. This is what we do all the time - we often know that someone is angry without actually waiting for them to say so - but we tend not to appreciate the extent of the effect. Those who study ideomotor phenomena can seem like telepaths. The classic case study is the horse, 'Clever Hans', who was able to answer complex numerical questions and yes-or-no questions by observing the behaviour of the person who asked him the question - assuming that the questioner (or his trainer in the audience) knew the answer themselves, the horse could give the right answer nine out of ten times. The person who worked this out then tried to emulate it himself, and discovered that he could be 90% accurate in deducing the answer to yes-or-no questions from the appearance of the person who asked the question.
In humans, going beyond obvious body language is difficult. It requires study and practice, and is still fairly limited in extent - you may be able to guess yes or no, or even have an idea what sort of things a person is thinking about (particular if you've primed them to respond in different ways), but true 'telepathy' is beyond us.
However, other species may have developed this to a more sophisticated level, to a point that actually does equate to telepathy. Then again, such a species would likely also develop the ability to lie through fine body language - humans aren't good at this, but largely because we've never had to be. So this wouldn't be telepathy in the circumvents-lying way. And if you want the signals to be read, you'll exaggerate them. So in fact what we'd actually see is basically just language, but conveyed through sign language rather than sound. However, if the signs are still quite subtle, an individual who has evolved to read them, and has developed an interest in humans and has applied their evolved hypersensitivity to small visual cues to human behaviour, would indeed seem like a mind-reader to a human audience.
Mesmerism, the induction of mental behaviours through the body language of the speaker, is rather more fanciful, but still sort-of believable. This wouldn't be so applicable to humans, though, unless the alien had evolved to influence humans, or had applied considerable study to the problem of how to do so.
However, mesmerism is in the realms of the highly improbable... rather than flat-out mental-influence-at-a-distance-through-EM, which so far as I can see is clearly in the realms of magic alone.
But the river tripped on her by and by, lapping
as though her heart was brook: Why, why, why! Weh, O weh
I'se so silly to be flowing but I no canna stay!