For cabled hard drives, you are required to power down the server and then replace the failed drive. Power back the server and monitor the rebuild progress.
Does it matter which of the two drives has failed? ie Does the resync always go from Drive 0 to Drive 1?
The synchronization process is not necessarily performed from hard drive 0 to 1 in RAID I array. It depends on which hard drive has the latest up to date data blocks and array time stamps.
How long should it take for a 7200 RPM 500 GB array to resync?
There isn't a defined time interval within which this process runs to completion. However, it is dependent on the size of the drives, RAID type, performance of the controller and I/O operations etc.
My understanding is that server needs to stay in the BIOS until rebuild is finished, it won't happen in background after server has started Windows.
Not necessarily. You can stay in the controller BIOS to monitor the rebuild progress when you do not have the OpenManage Server Administrator(OMSA) installed. The process will run while the server is up and running, no problem.