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!