Any space habitat of any plausible size will be completely undetectable, or at least indistinguishable from a planet. And I would think they'd be much smaller than that.
And structured radio? Lots of possible reasons not to see it. One, possibly not using radio. Two, encryption. Communication will likely look like noise. But even so, the distances involved means long range transmissions will need to be very directed and narrow beam. And even then, it's only a few light years before the signal is undetectable. I would suspect any really long distance communication would be bounced through relays. Also, why? You have to wait years for messages to go around. All of this means no, we're not likely to easily find stray radio signals.
And this is without getting into Dyson spheres and other efficient but detectable technology.
Yes, of course. And the heat of a star will make that heat completely invisible in comparison.
The "spectra" that heat would be vented at is infrared, which is infrared no matter the source.
Say you had some gargantuan fusion power harnessing space station in deep space. lots of assumptions here about alien cultures, but this is likely the easiest to detect. They will do whatever they do with their energy, and then vent the waste heat. That heat will be infrared. What does a dim infrared source look like (if even visible at all)? It looks like a brown dwarf. But this is assuming a lot. It assumes some alien would even build brown dwarf sized space stations. We don't know if or even why they would do that.
How do we know this? Because astronomers see these every single night and have developed sophisticated filters to remove them. But by checking how the source is moving it is quite easy to tell if source is local or not, and sure enough all these artificial sources come from satellites, the troposphere, or an unshielded microwave.
It is actually remarkably difficult and a challenging problem in itself to create a communication mechanism which looks like a natural source. It defies imagination to think that every single intelligent species out there has purposefully masked their existence in such a way, including giving up useful technology like ground control radar or mobile communications.
Just think about it. The signals are going to be so weak by the time the photons get here they will be indistinguishable from the CMB.
I'm sorry, but that's way off.
Our current telescopes can't even see the majority of the exoplanets in our galaxy; we are made aware of their existence by observing the behavior of their host star (wobbling/dimming). Unless something is extremely close, unfathomably enormous, or emitting/reflecting large amounts of electromagnetic radiation (light, radio, etc.) that isn't bent/filtered/reduced to noise, then we are completely unaware of it.
https://en.wikipedia.org/wiki/Dyson_sphere#Search_for_extra-...
It's like, nobody has considered that advanced life might not even feel a need to live on planets at all. It's expensive to get resources from, and there's a near limitless supply of easy to get smaller debris.
Additionally, the difference a 2 billion year head start could make is hard to imagine. One thing that's not hard to imagine is that they don't live in meat bodies for most of that time. They could easily be machines or virtual, and then would look and act nothing like anything we're looking for.