Unfortunately, none of the questions you asked are really answerable from the documentation we have. The kinds of record-keeping that would be necessary to answer these questions didn't begin until long after the Viking age: the pagan Norse were a literate culture, as attested by their use of the runes, but it was a very different sort of literacy, put to very different uses.

I can’t answer all of your questions, so I’ll focus on the aspects I am able to deal with properly: the question of the makeup of a "typical" fleet. This is an extremely difficult to answer, and could depend on any number of factors. Smaller warships, such as Skuldelev 5, accommodated about 30 men, while saga sources record the largest ships (such as Olafr Tryggvason's Ormrinn Langi) could supposedly carry 70 or more people. (Some of the more fanciful saga sources claim crews of a hundred or more, though that strikes many scholars as quite improbable.) How many men might we expect to have taken part in a raid? We unfortunately can’t say with any certainty. The Annales Xantenses claim that Viking armies were defeated in numbers ranging from 600 to 12.000 (Annales Xantenses, s.a. 845, ed. B. de Simson, MGH SS rer. Germ. (Hanover, 1909);) the lower estimate strikes me as far more likely. The earliest raids on undefended monasteries in the 8th-9th centuries could conceivably have been executed with no more than a hundred or two men; on the upper boundary, Olaf Tryggvason (an extraordinarily powerful warlord in his time, who was able to leverage his military strength to become the king of Norway) was able to command 93 ships when he raided England in 991, (Anglo-Saxon Chronicle, s.a. 993, in The Anglo-Saxon Chronicle: A Collaborative Edition, et. David Dumbille and Simon Keynes, trans. Swanton (Cambridge: Cambridge University Press, 1991,) 126,) probably putting his forces at somewhere between 3.000 - 4.000 men, by my own estimate. In the High Middle Ages, the kings of Norway were able to mobilize perhaps between about 14.000 and 30.000 men and about 350 ships via their naval levies (leiðang) (Sverre Bagge, From Viking Stronghold to Christian Kingdom, Copenhagen: Museum Tusculanum Press, 2010, 75-76. Bagge follows medieval manuscripts in estimating that 4-5 men might sit at a single ship’s bench, though some first-hand experience sailing reconstructed ships makes me doubt very much that this would be possible.)

As for how long a ship could stay at sea: well, that would depend very much on the size of its crew and the type of ship. The longest overseas voyages the Norse made (Norway-Iceland, Iceland-Greenland) could conceivably have lasted up to about a month, but such journeys would have been undertaken in wide-hulled cargo vessels rather than the more famous warships, with far fewer crew members (perhaps as few as a dozen or so.) The longest continuous overseas journey a warship would likely ever have to make would be the crossing from Norway to the British isles, which can be easily accomplished in under a week, at which point supplies would likely have been running low. To the best of my knowledge ships would have carried their own supplies with them, rather than relying on dedicated support vessels. (I can think of some saga sources to back this up and can find the citations for you when I’m at home, if you’re interested.)

Add’l Sources:

Brink, Stefan, and Neil Price, eds. The Viking World. New York: Routledge, 2008.

Jesch, Judith. Ships and Men in the Late Viking Age: The Vocabulary of Runic Inscriptions and Skaldic Verse. Woodbridge: Boydell and Brewer, 2001.

Winroth, Anders. The Conversion of Scandinavia: Vikings, Merchants, and Missionaries in the Remaking of Northern Europe. New Haven: Yale University Press, 2012.