J. Lee Graham

I'm really glad that the counterpoint threads here have inspired you. I believe - as does Brandon Homayouni, the author of the Fugue Challenge thread - that nothing will speed and hone your development as a composer quicker and more surely than this kind of exercise. I find that it opens up new areas of my artistic mind every time I attempt it.

To answer your questions, here's my input - others are more than welcome to add their own:

In the context of a symphonic development, a fugato is more appropriate in my opinion. It might typically consist of an exposition, an episode, and perhaps another full or partial exposition. Much more than that will be difficult to balance in the movement.
I don't think it matters how many voices you employ. There is something about four or five voices that is rather satisfying in a symphonic texture - the five voice fugato near the beginning of the finale of Mozart's 41st Symphony comes to mind - but a three voice fugato, while modest, will fit the bill nicely.
Doubling can be very effective and colourful. In the Classical period (which you are emulating) it was probably more common for the strings to perform the exposition alone and be joined by winds afterward (again, the Jupiter Symphony comes to mind), either doubling contrapuntal voices or reinforcing harmony, but use your best judgment; in Mozart's "Die Zauberfloete" overture, he brings in the bassoons to double the cellos when they enter in the exposition, and it's wonderful.
I would say that 1 woodwind to 1 string part would be the best doubling. I'd probably do it flute I + violin I, flute II + violin II in your case, maybe even with the flutes an octave higher if the string entrances are in a moderate register. For stylistic reasons, I wouldn't personally have the horns double anything...that kind of thing came later when horns were more flexible, but not in the classical period. If you had a bassoon, having it double the viola strengthens their line and adds colour, or having it double the cellos (and basses if they're on the same line) reinforces the bass. If you have a strong, penetrating woodwind (oboe, for example), it might take its own contrapuntal line.
That would be wonderful if you could make it work. Double fugues are exponentially more difficult. I haven't personally mastered double fugues yet - I have yet to make one work convincingly to my satisfaction. It's a great idea, though, and I wish you the best of luck if you decide to attempt it. Maybe you should practise first before trying to do it within a symphonic movement...you don't want to lose your virginity in a an S&M orgy, if you know what I mean.
Keep the overall structure of the symphonic movement in the back of your mind as you write the fugato in the development; it might be tempting to overdo it. I wouldn't overbalance the movement with too much in the development, unless what you have up until then and what you think you'll be doing afterward will balance it, either in length or by the weight of its character and subject matter. Classicism is all about order and balance. Indulgence in this area was the province of a later generation.

If you decide on a 3 voice fugato, it's going to have a Galant or Rococo feel about it...that texture was rather common in the 1740s and 50s. The authentic treatment would be to have the viola doubling the cellos and basses an octave higher for the exposition, then perhaps split off onto its own non-contrapuntal supporting line.

Above all, enjoy the process, and good luck to you! I look forward to hearing the result.