Either way, overlap happens, usually, due to differences in time preferences. All that is offered is 2 days, all that is requested is 30 days, for example, so no match occurs.
The order book would be easier to read if you separated out the time preferences into different order books. I.e. have a 2-day order book, a 30-day order book, etc. This would also make it more resemble conventional fixed-income instruments.
This exactly. Bonds are showed separately for a reason. Money has time-value. Money 2 days from now is worth different than money 30 days from now or 30 years from now. There's a whole science of trading yield curves.