I got interested by this question and did some research.

In terms of your first question, yes, it does appear to be generally agreed that the early Islamic world made extensive use of industrial mills and other machinery. ("Industrial mills" is used in contrast to "agricultural mills": agricultural mills mill grain, industrial mills do other things like saw wood or make paper pulp). The Ancient Romans used mills for sawing and forging, and the Chinese were automating bellows for iron furnaces in the 1st century BCE. There is extensive evidence of industrial mills for a wide variety of uses in the Middle East by the time of the Crusades, and it appears that improvements were circulating across the Mediterranean, the Middle East and out to China, and these improvements were conveyed to Western Europe (Lucas, pages 8-11).

Beyond mills specifically, to the best of my knowledge, the evidence is that the Islamic world saw economic growth over medieval times, though the topic is only starting to receive the sort of detailed quantitative work that has been going into the economic history of western Europe and Japan for decades. Of course, the scientific and literary output of the Islamic world has been known about for centuries, but there is evidence too of rising use of money, agricultural output, trade, finance and manufacturing, not just in terms of increased inputs but in terms of techniques (see Shatzmiller, 2011). On the other hand, Shatzmiller doesn't claim that GDP per capita in the early Islamic world was increasing at anything like the rate that it did in Britain from 1750-1850: the early Islamic world was prosperous in the way that China or the Mediterranean or France was at a similar time.

Was this an industrial revolution? The term "industrial revolution" has, to the best of my knowledge, never been given a widely accepted technical definition, unlike the term 'recession'. The New Palgrave Dictionary of Economics for example talks not about what is is, but what the term has come to mean.

Lucas's paper, with its discussion of the history of mills, was written to criticise claims of other historians of an Industrial Revolution in Medieval Europe: after surveying the evidence, he disagrees with the claim of a medieval European industrial revolution on the basis that there's a shortage of evidence that Europe generally was ahead of the Islamic or Chinese areas in this area, arguing instead that, if anything, Europe was behind, with the exception of some regions in France. This is consistent with my general understanding of how the term "Industrial Revolution" is used: it is more impressionistic and relative than precise.

Perhaps a useful metaphor here is architectural drawings of a house: you can look at the floor plan or the front elevation or the electrical wiring plan or a perspective drawing. They all show different information but none of them are wrong and each view has its uses. Similarly you can think of early Islamic economies (or Chinese, or French, or wherever) as being like 18th century Britain's or different to. Neither view is necessarily better than the other. Just one should always be aware of the chance of having picked up the plans for the wrong house.

Sources

Shatzmiller, M, 2011, Economic Performance and Economic Growth in the Early Islamic World, Journal of the Economic and Social History of the Orient 54 (2011) 132-184

Lucas, A. (2005). Industrial Milling in the Ancient and Medieval Worlds: A Survey of the Evidence for an Industrial Revolution in Medieval Europe. Technology and Culture, 46(1), 1-30. Retrieved May 27, 2020, from www.jstor.org/stable/40060793