In the top right of the video of a shuttle launch an astronaut has an open book resting on (attached to?) the left thigh. What was the purpose of this book? The astronaut then seems to take a pen or pencil with their right hand. How was pen/pencil secured for when they entered freefall? I'm assuming it was secured.
Those are the Ascent Checklist and the Ascent/Entry Systems Procedures (AESP) book. These are used by the back-seater Mission Specialists (MSs) and contain copies of the cue cards and flip-books used by the front-seater commander and pilot.
The MSs follow along in the checklists and back up the front seaters.
The Ascent Checklist contains the nominal and ascent abort procedures. The AESP contains malfunction procedures. Both are available at the JSC flight data file page: https://www.nasa.gov/centers/johnson/news/flightdatafiles/index.html