Bit late replying to this, but using a S*y Digital satellite dish for WiFi use is most certainly possible. Saying that it's been two or three years since I last experimented with it, which I'll talk about shortly.
Earlier this decade I moved into a flat which was reasonably high up on the edge of town with a good visual view of it. Experimenting with a USB WiFi adaptor showed that a weak but usable "free wifi" (that's free as in free beer) signal was detected at a window, so I bought for a couple of quid at a pound shop a mesh cake cover. Whilst not parabolic, adjusting the aerial on the WiFi dongle to poke through the middle-top of the cake cover gave a useful increase but was subject to periods of suddenly stopping for a couple of minutes before starting again. Not long afterwards I took an old 2 litre plastic bottle, covered one half of the round side of it with aluminium foil and placed a spare collinear 2.4GHz aerial roughly at its focus point to give something like a 2D parabolic crossed with a corner aerial. This worked very well picking up this free WiFi hotspot with far fewer dropouts than using the mesh cake cover and it kept me going for at least three months before I got ADSL installed (it was with S*y, please don't judge me, I was young, had little money and a new landline had to be installed that I only paid £10 for. I quit after the 12 months and I reckon I cost Sky more that what they took from me. So I've a clear conscience I reckon). In case you're wondering where the Free WiFi was coming from it was from a local McShite that was 320 metres (almost) line of sight to my flat window. Can't remember who was the provider at the time but they had outdoor coverage at ground level over a decent distance. Several months later they changed the free customer WiFi to O2 which had less outside overspill, and reception at my flat window with the 2L bottle aerial was down in signal strength to matching that of the unaided dongle of the previous provider.
Fast forward on a couple of years into my present abode and again it's quite high up compared to the surrounding area. One evening I decided to experiment with a S*y Zone 2 dish balanced on a chair looking out the window, with the LNB removed and the said dongle used for the initial flat tests positioned so its external aerial was roughly at the focus point (little adjustments made to try and get it right without fully succeeding). It was very much a ramshackle set up - the dish couldn't fully look "down" through the window and I didn't experiment with the dish upside down to compensate, and the simple monopole external aerial of the dongle certainly didn't "couple" well with the dish with its omnidirectional radiation pattern, but it did reasonably well. While the bare dongle aerial picked up between 7 and 9 APs depending which way the wind was blowing, the Zone 2 dish and dongle combo picked up 92 APs over a 15 minute period. One AP that was particularly noticed was that of my parent's BT Home Hub 3 router! That covered a line of sight distance of around 850 metres though it was weak (highest received signal level was -88dbm) and would have certainly have benefited by the dongle aerial having even a small amount of directivity towards the dish surface.
There's plenty of demos and write ups of using discarded and unused satellite dishes for WiFi point-to-point use though most examples seem to come from the USA or Canada. In fact I have not come across one that involves the use of a S*y dish, either Zone 1 or Zone 2. I suspect performance might be similar to the DirecTV and Dish satellite dishes that are a wide oval shape to take in multiple LNB focus'. One problem using these dishes or any offset dish is that with the 40mm standard Ku Band LNB neck size this is much to small to accommodate a waveguide that will operate on 2.4GHz, so a little imagination might be needed as to how to get the pick-up aerial to properly stay at the focus point. Quite popular is the use of "biquad antennas" at the focus point, some also use waveguides like "cantennas". Certainly a unidirectional aerial aimed at the dish surface will help matters more than a small omnidirectional one, though don't use something whose beam is so tight it can't see most of the dish!
As for dish sizes, I recall reading once (probably years ago in a copy of WotSat) that for a parabolic aerial to contribute gain it must be at least one wavelength in diameter of the lowest frequency that is intended to be received. If the parabolic surface is solid then it doesn't really matter what frequency it is being used on to help receive (mesh/perforated ones have some limitations) but the higher the frequency for the same given surface area, the higher the gain - but also the tighter the forward beam will be. From some very rough calculations a 45cm solid dish or Zone 1 dish can still give a decent gain over a simple monopole, though the gain achieved would be on a par with a good high-gain yagi-uda designed for frequency range. Once you started hitting dish sizes from around 70-75cm and bigger you then can get gain figures that'll outperform pretty much all yagi-uda's, in the region of a gain between 18-23dbi. For 5GHz WiFi, this gain will increase further albeit with a narrower forward beam.
One concern would be as to how you'd intend to feed the signal from the aerial at the focus point down to the transceiver. You could get away with say a USB dongle mounted on the dish which was then fed to a computer by using USB cables provided everything involved that's outdoors (except the dish itself) was suitably weatherproofed or rated for outdoor use. Power over Ethernet is another option if it allows. Coax cable is tricky given the losses at 2.4GHz and especially 5GHz. On the face of it the common WF100 coax cable might be OK for short-ish runs, the main problem being impedance matching but the loss of signal between an impedance of 50 ohms and 75 ohms mismatch is fairly marginal that in most cases for receiving it hardly matters - for transceiving with the 100mW EIRP power limit in the UK and most (all?) of Europe I'd say you're unlikely to damage the likes of dongles and access points through a high SWR (In theory a 50-75ohm mismatch will give a SWR reading of 1.5:1 which gives a fraction of a db loss). I must admit using 75Ohm cable for feeding WiFi isn't something I've done before so I might experiment doing it later this year. As mentioned, coax losses at 2.4GHz can be significant even though WF100 standard coax is now intended to carry frequencies up to 2.340GHz for Sky Q so probably best to limit it to a maximum of 10-12 metres before cable losses start being significant.
Maybe more later.