So it's possible to model what has already happened. When will this method allow us to do a reliable forecast?
Short term? I'd imagine 'never'. It's like, in layman terms (because I'm a layman

), forecasting the result of a coin-toss. You can toss the coin a million times, and it'll give you a good idea of the frequency of heads vs tails (I'm assuming tiny imperfections in the coin make this a non-50/50 chance, incidentally, otherwise it's a daft analogy) over time. But it won't give you a reliable indicator of the next toss.
How many ground stations are on Earth now?
Not sure. A cursory check shows - for example - 62 automatic and 4 manned in Hong Kong, and 11,000 co-operative observers (I'm not sure exactly what this means; FYI each weather station has a 6-digit identifier, but I'm not sure if this applies internationally) in the US. Greenland has 18. I believe, though, it is a known problem that places like Africa have too few automatic weather stations (by about 200)
The recommended density of these stations is one every 3250 square miles (Africa is every 26000); they all get linked as part of the
Global Climate Observing System.
This page gives a pretty neat indication of their spread.
Of course---it's further from the sun, but affected nonetheless.
But how affected? I mean, what's the theoretical maximum?
I don't know, but if I google "Pluto warming" I find many articles which state otherwise.
Well, if I search for the converse what I find is that the surface is warming
On the self-reinforcing thing, I ask again, has such a thing ever been proved to happen before?
Modelled, yes; I believe things like the Permian extinction have been attributed to it (in that case volcanic emissions). If what you're asking is whether it can be lab duplicated, you'd need a whole planet methinks before you could be definitive. But they have done studies and AFAIK there is no dispute that the earth goes through cycles of positive-feedback climate change (warm-cool-warm-etc), the dispute is a) is it happening justnow and b) if so is it down to human activity.
Possible yes, but isn't plausible a strong term? Occam's razor and all that.
I'm not sure Occams razor applies unless it's the simplest possible solution, and I think to say the same factor was affecting every planet would not be the simplest solution given that you're talking about 4 disparate bodies, seperated by significant orbital distance (with other inbetween), with massively different geological (Mars might not even be molten core, and as for jupiter..) compositions, different orbits (Mars is apparently undergoing a periodical wobble), and different atmospheric conditions (for example, heavy CO2 in Mars).
Apparently for Jupiter it isn't warming globally, anyways, but experiencing a 'migration' where the equator is becoming hotter and the poles cooler.
Also, it's particularly relevant for Pluto, because Pluto is one 'planet' definately affected by the sun simply because it's in such an elliptical orbit that its distance changes; insofar as I can see that's the simplest explanation and indeed the astronomers (etc) one, that the response of Pluto to this changing distance is simply a wee bit more complicated than anticipated.
(also, as Flip noted, Plutos inclination towards the sun changes, so this could be a seasonal affect)
Yes, but I don't know if the other satellites are being monitored or to what degree, so I can't say.
Well, how likely do you think it is?
I'm assuming you're referring to solar radiance here affecting 'all' (well, 4 planets, one of which is undergoing a Malinkovich cycle and the other of which isn't warming globally but regionally) the planets. But the warming on earth isn't in tandem with solar radiance;

(source;
http://www.mps.mpg.de/en/)