How close would Earth have to be for us to detect it was habitable, and then inhabited? Given our current technology (or technology that is near implementation), how close would a clone of our Solar System (and so also Earth) have to be to us in order to detect that the cloned Earth was in habitable, and also how close would we have to be to detect that there is life on the planet (excluding radio signals the cloned humans have broadcast into space)?
Basically I'm asking if we assume the worst case scenario where life only exists on Earth-like planets, and that the life is the same as ours (ie is inteligent, builds cities, etc), at what range with our current technology and methods/techniques would we be unable to detect a planet and civilisation the same as our own (seeing as it's the only civilisation we know about)?
EDIT: Another way to put this, assume every star system is identical to the Solar System, using our current technology/techniques what is the furthest planet we could "see" that is habitable, and what is the furthest planet we could "see" that is inhabited by a species identical to our own (so the identical Earth 500 lightyears away would actually be in the year 2513, so we'd "see" it in 2013).
 A: If we are assuming that we are restricted to observing them via light only, then we can use the angular resolution relation,
$$
\theta\approx1.22\frac{\lambda}{D}
$$
where $\theta$ is the angular resolution, $\lambda$ the wavelength observed, and $D$ the diameter of the aperture. Note that this only applies to optical and radio telescopes.
In order to observe a planet with such a telescope, we'd want something like nano-arcsecond resolution at a wavelength of $\lambda\sim500\,{\rm nm}$. This would give us an aperature diameter of about 600 meters, which simply doesn't exist.
We possibly could use something like the Very Long Baseline Array, but despite the separation of many km, even that has an angular resolution in the milli-arcsecond range in the needed wavelength range. Perhaps locating one on the moon and/or on Mars might give us the needed distance for the desired resolution?
A: I had put off answering this question because it seems too broad without specifying the proposed detection methods, and excluding radio signals seems crazy (so I have considered them). If we were to take the solar system and put it at the distance of the nearest other star, at present, it is unlikely we would we able to detect signs of life on planet Earth.

*

*No planets very similar to the Earth have yet been detected around another star. That is to say, none that have a similar mass, radius and orbit at 1 au (or close to it) from a solar-type star. With current technology, it is just out of reach. Therefore any directed search for life on Earth wouldn't actually know where to start. If you can't detect the planet at all then there is absolutely no chance of looking at its atmospheric composition to look for biomarkers (e.g. oxygen along with a reducing gas like methane, or chlorofluorocarbons from an industrial civilisation - Lin et al. 2014). The only exoplanets for which atmospheric compositions have been (crudely and tentatively) measured are "hot Jupiters". - giant exoplanets orbiting very close to their parent stars.


*If we were to look at the Sun and Solar System as "another star" then if we were lucky with the orientation and observed for long enough then we would be capable of detecting Venus and the Earth as "transiting planets". But we would need to observe for several years in order to confirm the repeating nature of what is a very small blip in the light curve. Detecting Earth and Venus via the Doppler method is currently impossible because of the limited sensitivity. Though this may change in the next decade or so, with ever-more stable spectrographs on large telescopes. At the moment we would detect Jupiter and Saturn (if we observed for long enough), but nothing else. One way of finessing these difficulties is to broaden the definition of "Earth-like planet". If we include those planets with an Earth-like mass and radius in the "habitable zone", then there are planets like this being found around low-mass stars. These are easier to find because they have shorter period orbits, with a bigger Doppler radial velocity signature and are more likely to transit.


*A "blind" search could look for radio signatures and of course this is what SETI has been doing. If we are talking about detecting "Earth", then we must assume that we are not talking about deliberate beamed attempts at communication, and so must rely on detecting random radio "chatter" and accidental signals generated by our civilisation.
The SETI Phoenix project was the most advanced search for radio signals from other intelligent life. Quoting from Cullers et al. (2000): "Typical signals, as opposed to out strongest signals fall below the detection threshold of most surveys, even if the signal were to originate from the nearest star". Quoting from Tarter (2001): "At current levels of sensitivity, targeted microwave searches could detect the equivalent power of strong TV transmitters at a distance of 1 light year (within which there are no other stars)...". The equivocation in these statements is due to the fact that we do emit stronger beamed signals in certain well-defined directions, for example to conduct metrology in the solar system using radar. Such signals have been calculated to be observable over a thousand light years or more. But these signals are brief, beamed into an extremely narrow angle and unlikely to be repeated. You would have to be very lucky to be observing in the right direction at the right time if you were performing targeted searches.
Hence my assertion that with current methods and telescopes there is not much chance of success. But of course technology advances and in the next 10-20 years there may be better opportunities.
The first step in a directed search would be to find planets like Earth. The first major opportunity will be with the TESS spacecraft, launching in 2017, capable of detecting earth-sized planets around the brightest 500,000 stars. However, it's 2-year mission would limit the ability to detect an Earth-analogue. The best bet for finding true Earth-analogues will come later (2025 perhaps) with the launch of Plato, a six-year mission that again, studies the brightest stars. However, there is then a big leap forward required to perform studies of the atmospheres of these planets. Direct imaging and spectroscopy would probably require space-borne nulling interferometers; indirect observations of phase-effects and transmission spectroscopy through an exoplanet atmosphere does not require great angular resolution, just massive precision and collecting area. Spectroscopy of something the size of Earth around a normal star will probably require a bigger successor to the James Webb Space Telescope (JWST - launch  2024?), or even more collecting area than will be provided by the E-ELT in the next decade. For example Snellen (2013) argues it would take 80-400 transits-worth of exposure time (i.e. 80-400 years!) to detect the biomarker signal of an Earth-analogue with the E-ELT!
It has been suggested that new radio telescope projects and technology like the Square Kilometre Array may be capable of serendipitously detecting radio "chatter" out to distances of 50 pc ($\sim 150$ light years) - see Loeb & Zaldarriaga (2007). This array, due to begin full operation some time after 2025 could also monitor a multitude of directions at once for beamed signals. A good overview of what might be possible in the near future is given by Tarter et al. (2009).
