Well, in a simple minded way I can see an obvious answer. If, by pushing a little innovation, they can reduce the cost from $2k to $300, that's a 6x reduction in cost. When multiplied by, oh, the entire U.S. military population, that becomes a substantial dollar amount.

For receiving only, a long-wire antenna should work fine.

Until we went to the Moon via Apollo and found the subtle differences in composition of the rocks, when compared to Earth, the leading theory was that it formed simultaneously with Earth as a kind of dual planet.

Nuking the Moon won't get anyone's attention, it'll just create more mess.

The 3rd rock around this star draws attention because it has copious liquid water, free oxygen in its atmosphere, and has both artificially produced light and sub-atomic particles emitting from it's surface. That should be more than enough to get someone's attention, if they happen to fly by.

Well, there might be a thin atmosphere composed of stuff boiling off the star facing side.

If it's that close, it's likely tidally locked, or at least have a very slow rotation as does Mercury; so, the "dark side" should stay icy.

There have been a number of planets found orbiting binary star systems. Kepler has identified a planet around a star in a binary pair, orbited much further out by another binary pair.

We collected shiny things before writing was invented... But there just weren't enough people picking up shiny rocks to have a significant impact on the available quantities. You are correct though: used to be you could walk up to a stream bed and find "precious" metals and stones just sitting there.

Will turn out to be a chunk of platinum group metals. So begins the push to mine Mars.

What do you do when the rotation has to be shut down? Picture, things have gone to shit. Station is in danger. They had to shut down the rotation to effect repairs on the structure. And you have a triage ward full of victims... You'll need a zero-gee backup plan, even if that's not your primary and preferred methodology.

Fundamental laws of physics apply, even if you're a technologically advanced civilization.

Aliens from Independance Day. Essentially swarms of inter-stellar locust, consuming all natural resources on a planet, then moving on...

Maybe. But maybe it takes so much energy to bring the other power sources to fruition that you need a massive source of energy to begin with; and, it's only worth the effort to power things like ships that need more compact energy sources.

Taking a cue from science fiction: If I remember right, in Star Trek lore, the Federation gets it's supply of anti-matter from a particle accelerator built on a platform in close orbit of Sol. It extracts the energy necessary to run the process from the star. It's not efficient; so, the only place it's worth using is to power starships. They use more mundane methods to generate power for use on the planet surface.

You should be careful what you ask for. There are things you really shouldn't poke with a stick -- Bears for one, large cats, wasp nests, hives of locusts... Aliens advanced and hungry enough for raw energy (and materials) to build Dyson spheres.

OK, there are two issues here to discuss...

You could certainly build fusion power plants. Lots of them. As your power requirements go up as a society, you just build more. Except... The waste heat. No power generation process is 100% efficient. In fact, 30% may be a reasonable number for a nuclear plant. The remaining 70% becomes waste heat dumped into the environment. Now, what happens to the electrical energy you made -- the 30%? Some of that will get turned into "stuff" or into forms of potential energy. A substantial fraction will likely get converted into heat. So, as you build more and more power plants, you put more and more heat into the environment. You can already see this in localized heating of rivers where power plants draw water for cooling. If society becomes orders of magnitude more energy intensive than we are now, the heating of the environment could become a significant problem; and, the same would apply to any hypothetical advanced alien society.

As to where you get the material to build a Dyson sphere... To begin with that's a misnomer. No one would build a sphere -- they'd build a ring or a large number of orbiting platforms. As you pointed out, the solar system is vast. If your society is becoming advanced enough, large enough and energy intensive enough that you might consider a Dyson sphere, then you're probably going to have (or be able to develop) the ability to mine the non-habitable planets, asteroids, etc. for the raw materials you need.