Short answers, pulled from the story.
The spinning jenny was invented around 1764 and is attributed to James Hargreaves in Stanhill, near Blackburn, Lancashire. It was an adaptation of the spinning wheel designed to spin multiple threads at once.
The water frame, developed and patented by Richard Arkwright in the 1770s, used drafting rollers and a spindle in a continuous motion and could only spin yarn twisted to the left. The spinning mule, created by Samuel Crompton in 1779, combined the water frame and the spinning jenny in an intermittent process, making it capable of spinning a wider range of yarn counts.
The spinning mule became fully self-acting in the 1830s. Between 1824 and 1830, Richard Roberts invented a mechanism that regulated all parts of the mule automatically during the inward run of the carriage.
Lewis Paul and John Wyatt were Birmingham inventors who in 1738 patented the Roller Spinning machine and a flyer-and-bobbin system. Their design used two sets of rollers at different speeds to draw cotton to a more even thickness and became the basis for Richard Arkwright's later water frame.
Open-end spinning, also called rotor or break spinning, is a high-productivity method that feeds fiber slivers directly and eliminates the roving stage. The first commercially successful rotor spinning machines appeared in the late 1950s and early 1960s, introduced notably by Rieter and other European manufacturers.
DREF spinning is a friction-based open-end spinning system developed by Dr. Ernst Fehrer in Austria in the 1970s. The first commercial DREF-II machines were introduced in 1973 and were designed for very coarse yarns, technical textiles, and core-sheath structures rather than apparel-grade yarn.