Yes, producers have always had the incentive to innovate, and yes, they have always tried to do so (even slave economies were "capitalist"). Only in certain institutional, cultural, and geographical contexts can they be successful. I also think base levels of scientific knowledge are critical (but Anton may disagree in some cases).
As for demand, I refer you to Mokyr's classic piece: http://www.jstor.org/stable/2119351.
So, sort of. Everything is endogenous. Desmet and Parente argue that market expansion leads to longer firm production runs in differentiated goods and lower per unit fixed costs (thus process innovation). But why was there market expansion in the first place? Population growth and foreign trade? In the latter case, I'm going to be working on this for a long time yet. But it's important to note that the UK TOT fell during the IR. Supply was outpacing demand in textiles.
Historian's perspective: the Industrial Revolution was primarily a supply-side phenomenon. Demand may have helped to geographically focus the concentration of new sectors, but technological change occurred because of the desire of producers to make things better and at lower cost, not because idiot peasants realized that cotton clothes were comfortable. Other factors—science, bourgeois/Protestant ethic, coal/raw materials, skills—are also supply side.
Neither necessity nor desire is the mother of invention!
Ha, I wish. Maybe a children's illustrated encyclopedia.
Market expansion is definitely an interesting area for research here. Foreign trade shares in the economy were small, but in certain key sectors (i.e. textiles) it was pretty significant. But again, it's important to unravel whether these markets can be considered A) additional demand or B) won by higher-quality / lower-cost production. That's the story of the "New Draperies" in the 17th c. and cottons from the 18th.
Anton and I have chatted about this a lot, and I agree with most of this. "Labor push" is a thing, but more for 20th-century developing economies than for first-wave industrializers. See Alvarez-Cuadrado, Francisco, and Markus Poschke. 2011. "Structural Change Out of Agriculture: Labor Push versus Labor Pull." American Economic Journal: Macroeconomics, 3 (3): 127-58.
I think you've hit the nail on the head—the fifteenth century is critical in the formation of (early) modernity. David Wootton argues that the Age of Discovery invented the idea of discovery/novelty/invention, and I would love to investigate this idea further. Even beyond the technical challenges of navigation, the notion—which anyone can understand—that there are new things in the world outside the current bounds of human knowledge is critical for getting people to seek out and trust new technologies.