Is it possible to restore a single file (e.g. my Aperture library) from a Time Machine backup when I reinstall the OS?
I want a fresh install and not restore the whole system from backup.
Sure, you can access your Time Machine backups, they're just files and folders.
Hold down Option while clicking the Time Machine icon. That will change "Enter Time Machine" into "Browse Other Time Machine Disks". Find whatever you want to restore there.
(Alternatively, why not restore your whole account? That's an option during a brand new installation. And note that OS X 10.5.3 or newer is required for a reliable backup!)