Does anyone know what exactly is their plan, once they get there? How is that nano-thing going to slow down / take images / send data back to us? I couldn't find any information on this.
There seems to be very little published information at this stage.
There is a main page that has been set up for the initiative (Yuri Milner's Breakthrough Foundation).
There's an interesting roadmap document too.
As for slowing down - no chance. As a page linked from the Challenges list says:
The nanocraft would traverse a distance of 1 AU in about 2500 seconds. To stabilize the image, the camera would need to “slew” at this rate.
For reporting back from Alpha Centauri, the roadmap's pages 25-26 and figure 20 predict that an onboard 10 watt laser with narrow spread (and many assumptions, such as at most 40 photons per bit) could transmit from Alpha Centauri to a 30 m reflector mirror on Earth at 70 Mbps.
But the power source for a 10 W transmitter is heavy!
Plutonium-238's power density is 0.54 watts per gram, so sustained 10 W transmission needs an RTG of at least 18 grams. (Materials with more power density, such as polonium-210, would run out of power well before the end of the 20-year voyage.) Burst transmission could be lighter, accumulating the RTG's electrical energy in a supercapacitor, which stores 15 Wh/kg. So a 1 gram supercap stores 54 watt-seconds, enough for a 10 watt 5-second burst transmission; a 1-gram RTG would result in a duty cycle of 1:18, in other words 4 Mbps sustained from Alpha Centauri. But even that compromise of a power source weighs much more than the spacecraft.
More likely is an RTG+supercap a hundred times lighter, 0.02 grams. That gives an upper bound of 40 Kbps from Alpha Centauri. Because the bottleneck is that single 30 m mirror, if the swarm can stagger its broadcasts in sync, and if the mirror can switch its aim from one spacecraft to another fast enough, that number could become 40 Kbps per spacecraft, however many survive the voyage. (Edit: seen from Earth, the spacecraft won't have spread out enough to need re-aiming. They'll appear to be transmitting from the same point.)
(Less likely is replacing the RTG with a nonrechargeable battery, needed only at the destination. The longest shelf life we know of is 10 years, not nearly enough. Likewise, although a stored chemical energy propulsion system aka SCEPS has excellent shelf life, it hasn't yet scaled down even to Mars Rover size, nevermind milligram size.
Edit: Gram-size SCEPS have been attempted. Kyle Jiang at U. Birmingham built a millimeter-scale gasoline engine 15 years ago, but abandoned it because of technical difficulties. Around the same time, U. Berkeley built a gram-size 2.5 W butane-powered Wankel engine, and built parts for a 1 mm version (milligram-size), but nothing else that small.
For comparison, New Horizons transmitted from Jupiter at 38 Kbps, and from Pluto at 1 Kbps. Too bad NASA didn't build a giant receiving antenna for that, instead of waiting many years for its stored data to trickle back via radio.
So the full report back from A.C. could take many years.
They don't propose slowing down, which is part of why they don't expect high resolution. In fact, they seem to expect most of the acceleration will occur from the beginning, by the time they hit Pluto's orbit, they expect them to be going at a very high speed.
The communication is expected to be done via lasers. Maybe they can re-convert their reflective shield to assist in improving the laser focus, to increase the power received.
Last interesting bit is they are expected to remain in hibernation until they make their final approach, making communication during the deep void virtually impossible.
Solar sails often suggest a couple of modes for slowing down.
1) Have a launch laser at the target location to slow it down the same way. Assumes much infrastructure.
2) Use the solar energy of the target sun to slow the sail down. I.e. Turn it around and spend a longer time decelerating as you get closer and closer.
3) There was a model, where the main sail had a second larger sail that would fly with it, during acceleration, but upon cruise would separate, and advance in front of the main sail. Then the launch laser would target the larger sail, to reflect the energy back on the smaller sail to slow it down. (Lots of tricky bits in that approach).