Round here is a contraction of around . He slept around the clock (meaning many hours as the clock hands went around, marking out the time - this of course goes back to the days of analogue clocks where the hands physically turned around the circle of the clock face!). 'I want you to keep watch round the clock' - meaning continuously, at all hours. The usages you have written above don't sound quite right. These would sound more natural:
She read throughout the morning (meaning for the whole time of the morning)
she read for the whole morning
she spent the whole morning reading