Some numbers come from a review paper by Cullers (2000), who discusses the SETI Phoenix project. There, it is claimed that the Arecibo dish is capable of detecting a narrow band, coherent signal of $f=10^{-27}$ W/m$^2$ given a 1000 second observation. Assuming that this is an isotropic signal, then the implied power at distance $d$ is $p=4\pi d^2 f$, which means that $p \simeq d^2$ MW.
So, it is clear that unless a 1MW signal is highly beamed it could not be detected by our current technology even from a nearby star. (Actually, this number is out of date, the receiver at Arecibo is somewhat more sensitive now, but I can't find any numbers).
Of course we do emit more beamed signals. The Arecibo radar transmits at 1MW, but its equivalent isotropically radiated power is 20 TW. In other words, the Arecibo dish could detect the directed signals it emits (and of course does, when performing solar system metrology) at distances of about 5000 light years although the radar does not normally send a signal for 1000s.
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.".
A recent survey using the Green Bank telescope was able to rule out continuous signals (between 1.1 and 1.9 GHz) at the level of 8 (beamed) Arecibo radars from a large sample of 104 Kepler planet hosts at distances of ~1000 light years.
The next generation of radio telescopes use "phased arrays" to monitor signals from many directions at once and can perform wide-angle surveys much more rapidly. The SETI project is now using the Allen Telescope Array. The claim is that over 10 years it can survey a million stars with sufficient sensitivity to detect the Arecibo radar out to distances of 1000 light years.
It has been suggested that new radio telescope projects and technology like LOFAR and the Square Kilometre Array may be capable (using a month or so of observing time) of serendipitously detecting radio "chatter" at a few hundred MHz out to distances of 10-1000 light years and over a fair fraction of the sky - see Loeb & Zaldarriaga (2007). The SKA 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).
EDIT: I realised I didn't fully address the question. The Arecibo dish can detect the beamed signal you talk about in 1000s at a distance of about 5000 light years. The dish has a diameter of 304m. So to detect a signal that comes from 5 times further away which will be 25 times weaker would naively require a 1.5km dish (assuming the noise levels remain the same).
A motive is: "Seen from the front or rear of a handset user, the polarization will be dominated by the vertical component (the most handsets have a linear polarization because they use patch or monopole antennas), but in the lateral direction a handset is typically held at a large angle to the vertical, between the mouth and the ear of the standing or seated user, typically at least 45°."
Antennas for base station in wireless communications, Zhi Ning Chen and Kwai-Man Luk. pp. 40
Best Answer
1) Normally, the antenna isn't the only component that distinguishes between the various competing signals received. The antenna does have a bandwidth and will attenuate signals outside that band. A typical antenna on a cell phone mast for example, may receive in the range 1.8GHz - 2.4GHz (just an example, you would have to look up manufacturer data sheets for more accurate figures).
However the principal component that rejects competing signals in other frequencies is the filter. This is a tunable component that can be tuned to the frequency you wish to receive at any particular time and will strongly reject other signals.
There are other ways of transmitting signals to multiple cell phones (for example) than using different frequencies. Code Division Multiple Access is an example.
2 The most obvious way to disrupt signals is to transmit a high power signal on the same frequency band that the target signal is using.
3 An antenna may have a set of directions for which it is designed to achieve maximum gain. This directionality is encapsulated in the antennas gain pattern. The maximum achievable distance between an transmitter and receiver is a function of many things: The transmit and receive antenna gain patterns, the receiver sensitivity, the transmit signal power, the propagation loss... The calculation of these effects is called a link budget.