Or, let me ask otherwise, is it known what is the star closest to our Sun and similar to it in mass, age, and luminosity? What is the distance to it?
I can answer this part, not the UFO part.
Alpha Centauri A and B, the closest stars to the Sun after Proxima Centauri, are the closest Sun-like stars. A is a G2 star, just like our Sun; B is a K1 V star - a bit cooler, but still similar.
Here are some comparisons:
Mass
Sun - $1 \text{ M}_{\odot}$; A - $1.1 \text{ M}_{\odot}$, B - $0.9 \text{ M}_{\odot}$
Luminosity
Sun - $1 \text{ L}_{\odot}$; A - $1.5 \text{ L}_{\odot}$, B - $0.5 \text{ L}_{\odot}$
Photosphere temperature
Sun - 5778 K; A - 5790 K, B - 5260 K
Those numbers are really, really similar. And the system is only 4.37 light-years away.
If you want a really good solar analog, though, you have to go a bit further. Epsilon Eridani is your best option. It's 10.5 light-year away - a lot further than Alpha Centauri - and it's a K2V star; it's actually not a lot like the Sun. It appears to have an exoplanet, though.
Of course, there is some discussion of an exoplanet around Alpha Centauri B, too, but the claims have not been fully substantiated. The reason that the Alpha Centauri system isn't the best for life is that it's a binary star system - which we're clearly not in! Either A or B by itself would be a good starting point for a solar system; together, they aren't.
Even more exciting than Epsilon Eridani is Tau Ceti, a G-type star which may have up to five exoplanets and perhaps even a few in the habitable zone. It's 12 light-years away and has a huge debris disk around it, which could be an issue for life. But still, it's not too bad.