I'd be thinking something more like Venus. That planet is known as Earth's sister or twin. Of course we know it as pretty uninhabitable due to raining acid, thick atmosphere, and very hot surface temperatures. But it has an atmosphere, it has rocky landmasses, it had "water", etc. So in many respects it is very similar to Earth. Venus doesn't have any moons, but other planets out there could have close moons which could make them "tidally locked." Mercury is gravitationally locked with the sun in a unique way; "It rotates on its axis exactly three times for every two revolutions it makes around the Sun." Furthermore, "An observer on Mercury would therefore see only one day every two years."
If Venus had much less greenhouse gasses however, the temperature would drop, and the poles would eventually cool to a more reasonable level. So if there were a planet like Venus (but "tamer"), not exactly habitable by the society's consensus (and perhaps their particular physiology), but totally habitable by the aliens... then they could use that. Perhaps even work to terraform it by scrubbing out some of the greenhouse gasses to make it a little cooler. (Interesting result if society notices this, and starts looking at it more closely...)
Incidentally, the reason Humans likely haven't considered robotic terraforming of Venus is that it doesn't have a magnetosphere. Without that, solar radiation will reach the surface and strip off any water present (as well as slowly kill living things (as we know it) via radiation poisoning.
Keep in mind that days are determined by the planet's axial rotational velocity, and may vary greatly, as we've seen with Mercury. Years are it's orbital velocity around the star, and as @DJMethaneMan illustrated, do not have to follow the 365/1 Earth ratio at all. (But of course, planets with bigger orbits will generally have longer years, simply because the distance is further -- and likewise, smaller orbits = shorter years.) Here is an interesting comparison of the lengths of a "day" on our various planets.
Would this world be detectable from Earth prior to the invention of the telescope?
World, yes. Colony, not a chance.
Would it be particularly difficult to study and image the surface using today's technology?
Not really. We've already sent probes to peer at all of our planets. we have some great scans and photos. But they are orbital photos; without very high resolution, there is little hope of "spotting" a small settlement. "Spy satellites" are generally in a very low orbit, and use extremely high resolution.
Can I assume that a lander and orbiter would be totally out of the question for many decades too?
I can't answer this. If humans detected something on Mars 25 years ago, it would already have been investigated many times, likely with astronauts on their way there now for a little "meet and greet."
Would the sun's influence somehow interfere with communication?
Very likely. Solar radiation "flares", even protected by the Earth's magnetosphere, still manage to get through some and wreak havoc with many electronic devices occasionally. On a planet with no magnetosphere and closer to the sun, it might very well destroy electrical things outright, or "burn" skin, like a chemical or heat burn (which won't heal.)