Presuming you are not thinking of Tesla's work on resonant inductive coupling (like a Tesla coil), you are probably thinking of Wardenclyffe tower. That was suppose to be a ground - air conduction system. Many people incorrectly think it is an induction or radio system.

If you think about a classic circuit, electricity flow into one end, round the circuit and returns to the source at a lower voltage.

If you put a button and buzzer into this circuit and stretch to many kilometres / miles you have a telegraph.

The problem with this is your wire has to travel the distance twice. Once when it comes from the source through the button to your buzzer and then it has to go all the way back to complete the circuit.

But people eventually noticed you didn't need to do that. If the wire went into ground after buzzer, telegraph still worked. It was believed the circuit was completed through the Earth. It was also believed that the atmosphere had an extremely good conducting layer that was separated from the Earth. So this is basically two wires.

So the idea was to feed electricity into the ground, it would travel through the Earth, you would put a wire into the ground going through what ever you want to power, and the electricity would flow into the sky and back to Wardenclyffe tower completing the circuit.

This would allow relatively large amounts of energy anywhere on the planet as long as you had a wire. And would have been truly transformational to humanity.

But this doesn't work. We now know that the ground flow rate is extremely limited and drops off fast. But Earth has significant capacitance. So the telegraph lines were just feeding charge into that. The amount that telegraph lines used was low enough that the slow discharge rate didn't impact it that much. That capacitance gets used today with neutral and grounding / earthing lines, they just go into the ground. AC pushes and pulls that capacitance without needing a return path.

So Tesla's idea (and other people who attempted similar) ultimately wouldn't work.

Tesla however did work on resonant inductive coupling which is used on modern wireless power transfer systems, just no where near the scale of what Wardenclyffe tower was meant to achieve. It is extremely short ranged, normally used in lower power embedded circuitry but does have some larger use cases like magnetically levitating vehicles and the Tesla coil.

Yes. In current understanding distance doesn't matter. It could be few atom widths apart or light years. The fact that distance doesn't matter is one of the very interesting things about it and why there was some resistance to it (notably from Einstein) when the idea was first introduced.

Entanglement is a fancy way of saying the properties of two or more things rely on each other.

Imagine I have 10 balls which I'm going to put into two bags. I might put 3 in one and 7 in the other or 1 in one bag and 9 in the other. You don't know what I'm going to do, only that I will put all 10 balls in the bags.

Now imagine I gave a bag to you and you looked inside to find 6 balls. Since you know there are 10 balls in total you know the second bag must have 4.

These two bags are entangled as they have a property that relies on the other. This is mundane and isn't interesting at macroscopic level.

If we go smaller though we run into some more interesting things as things act less like solid things and more like waves.

So imagine I showed you a video of a wave in the sea. You could from that video see how fast the wave is moving but if I asked you to point to where the wave is that becomes slightly harder. The wave was in many places in that video because it was moving. (ok this simplified but just go with it)

If I showed you a picture of a wave. It would be easy to point to where it is. But if I asked you for the speed of that wave, that becomes hard.

As you can see the more we know about movement of something the less we know about its position. And the more we know about position the less we know about movement. This is uncertainty principle.

(Obviously that is simplified for the metaphor, but it is close enough in principle to how it drops out of the math. Just know that in the math, knowing more about one thing and less about the other is much more like a hard rule that must be obeyed than the metaphor implies. So following that principle is super important)

Now particle act a lot likes waves. The more I know about a position the less I know about its velocity. The more I know about its movement the less I know about where it is.

Think of our bag metaphor, imagine if the one bag was red balls only and the yellow balls only. You can either feel the bag to count the balls or open the bag to check the color of one ball. (presume there is always at least 1 in the bag). You will only ever know 1 property, but once tested you'll know it for both bags.

But what if you tested one bag for one and the other bag for another. So the one had 6 balls and other bag is yellow. Which means the bag has 6 red balls. Now I know two properties of one thing. But this isn't allowed by uncertainty principle.

To think of it in waves or particles. I check where something is (and know nothing about its movement) and then I check its counterpart's movement. Since I know velocity like the balls is shared between the two, I know the particles movement and position.

This isn't allowed so what happens?

First know that at the small scale things become probabilistic. You look in your bag and you have 6 balls. Look again now you have 5. Look again now you 7. Again 6, again 6 again 6 again 8. It's probabilistic, it is most likely going to be 6 but it could also be 5-7 and maybe even 4-8, even more unlikely but it could even be 1 or 2.

This is where the wave properties comes from, if you draw probabilities on a graph, you would see high point at 6 and it slows away like a wave. This is superposition (because it could be considered multiple things at the time) and where you check its wave-function collapse (because wave goes away and it becomes a thing) and also where all the talk about multiple things at the same time comes from. (bit more complex in practice but simplified it is reasonably accurate)

Now here is the "spooky action at a distance" or the part where everybody freaks out. The other bag was entangled. Every time you check the other bag somehow knows what value the bag you check has. If it 6 the other bag knows it must have 4 balls. But if you check again it has 5 and so the second has 5. If it is red it must be yellow. But you check again now you are yellow and the second knows to be red.

How does it know that? And how can it transfer that faster than light. You can't transfer information this way because you have no control of what answer your test will give.

But that is what entanglement is. One way this forms is if a particle decays into 2 or more particles. Those particles would be entangled because the velocity is shared between them.

In practice it is even more interesting because there are other quantum phenomena which interact with this to produce even more interesting phenomena.