I'm no forensics expert, but I have a friend who is a tech in a DNA research lab.
1. Without attached skin or the follicle, a hair is useless for DNA testing. That said, if there are already hairs in evidence, there's other things that can be done for a match besides DNA (comparison microscope comes to mind easily).
2. Depending on what kind of sequencing they're doing, the test itself takes from 12 to 36 hours to run (IIRC). HOWEVER, 99.9% of the labs are extremely backed up in the workload, which is why it can take days, weeks, months to get results back. From what I understand, if your right people know their right people, you can get a quicker turnaround time, but standardly it takes a couple-three weeks at best to get results back from what I've heard.
So, basically, you can make it work for your story however you want it to happen--but don't take your guidance from CSI. Their labs are someone's wetdream from all I've heard from my friends in the field.