Nina Kulagina etc.
I couldn't wear digital watches in my youth myself as they blanked out as soon as I got agitated or under physical stress- reproducibly. The effect was equal to what you would see when you put your watch against the magnet at the back of a big loudspeaker.
On a science fair I was measured, just for the heck of it, with a device that senses the strength and reach of magnetic fields. A magnetic field can be measured around every living thing as he demonstrated with his installation, and the scientist claimed my 'output' was in the range of 20 times what other people would show- while I was totally calm.
Later as adult I tried again and it seems that the effect was still there, albeit weaker (cheap and older watches behaved erratically but did not always blank out completely), and more modern watches were less or not at all affected. I haven't tried in years now, though.
I have a reputation however to always get the "Monday" models of every cell phone I use. They crash significantly more often that with colleagues and friends and 'die' faster...
Even today I don't wear watches or any kind of jewelery (not even a ring although I would have reason) as the metal on my skin makes me feel uncomfortable.
Also, as a child I was highly sensitive to electronic equipment. I slept in the middle of the room to be as far as possible of all electric sockets, and had all electric equipment unplugged at night. My parents installed a special device that disconnected the electric wiring in the house from the switchboard in the basement when no electric device was powered on- those with a transformer that kept sucking juice had to be physically unplugged.
If I slept too close to a socket or an "active" piece of tech I suffered heat rushes, bad sleep and nightmares, and woke up all sore and tense- again, reproducibly. When I slept at a strange place and had a especially hard time I would for sure find a wall socket covered by the bed I was lying on, and I moved the bedding on the floor.
As I grew up in the country side it was fairly easy to avoid the presence of electronic equipment. Then after moving to the city in my 20ties I had a tough time at first as it was simply impossible to avoid being close to electric equipment and installations, not only larger in numbers but also in size and "output". But the adverse effects diminished eventually, and after a two year period of slowly seizing discomfort I seem to have "adapted" or got desensitized. I don't feel any influence whatsoever from electronic installations anymore.
So if you ask me if humans can be sensitive to (electro)-magnetism and what new-agers call "electrosmog" I can assure you from personal experience: very much so. Does it cause you permanent harm? Don't think so, we are a very adaptable species.
Can we influence electronic equipment in some way? It seems so that some do if the equipment is sensitive and "vulnerable" enough.
Is it the bases for extraordinary abilities? Just "do the math"- check the physics, and especially the scale of power that at maximum _could_ be involved/"generated" and compare them to those that would be needed to affect "real world matter"- 'nuff said...