1. It can be built incrementally. What you'd probably do is build orbitals and put them in Earth's orbit around the Sun, Then you can keep adding new orbits. Ultimately you end up with a "cloud" of orbitals that will block a star's light in the same way that water molecules in a fog block light;
2. A likely candidate for an orbital is waht's called an O'Neil Cylinder: 3-4 miles in diameter, 10-20 miles long, producing Earthlike gravity on the interior by spinning. Smaller than this and it needs to spin too fast. Larger than this and you need stronger materials to stop it ripping itself apart from centrifugal forces. Stainless steel is sufficiently strong to build an O'Neil Cylinder;
3. Solar power is the most likely source for our future energy needs. It's the only known power source that directly creates power and it does so with no moving parts and no waste produced. In space, solar is so ridiculously efficient that it's unlikely fission could ever compete economically and fusion is still a pipe dream.
4. Approximately 1 in 10^9 of the Sun's output hits the EArth. That's an awful lot of "free" energy just radiating out into space. The growth potential is huge. What do we need all that energy for? History has shown we'll find a use but here's a big one: the energy cost of interstellar travel is so mind-boggling large that we'd need something like the Sun's energy output to do it. Plus an interstellar generation ship looks an awful lot like an O'Neil Cylinder.
Anyway, the article doesn't really explain why the seaerch for infrared radiation that I could see (maybe I missed it?). It's important.
A body in space like an O'Neil Cylinder will heat up, even with converting some of that energy to electricity. The only way to cool down in space is to either expel mater, which doesn't really scale, or to radiate it away into space. The wavelength of light from a radiating body is determined entirely by the temperature of that body and for any temperature we're likely to see, that means infrared radiation.
So if you look at a star with a near total Dyson Swarm you'll see much less visible light and much more IR radiation and there's really no way to hide that. Some might say you can capture the heat an turn it into energy but you can't do that with perfect efficiency (ie thermodynamics) plus the material of the orbital will just naturally radiate anyway no matter what you do.
It's extremely conservative to say that we'll have the technology to build and deploy an O'Neil Cylinder within 1000 years. Give it 10,000 years if you really want. It makes no difference. That's still the blink of an eye in cosmic terms. And that gap between having 1 and a billion is also the blink of an eye.
And once you have what's called a K2 (Kardashev-2) civilization (being one that uses the full energy output of a star) where interstellar travel becomes possible, even practical, seeding a new Dyson Swarm around another star becomes trivial and the proces continues to the point where 100 million years from now is a completely realistic time period to have a Dyson Swarm around every star in our galaxy.
A galaxy of Dyson Swarms would be so obvious to observers even millions of light years away, even at our current level of technology. The absence of seeing such a thing contributes to the idea that spacefaring life is incredibly rare.