I'll disagree a bit. The RAID system in your BIOS is still a software system - it uses your mobo's HDD controller chip and some CPU time to do the work. A true "Hardware RAID" system has its own dedicated processor chip, its own BIOS and some RAM to do the work, and usually these come on a card plugged into a PCIe slot.
But that small point aside, I would advise using the BIOS' RAID rather than Windows' software RAID. The BIOS version usually is better and tuned to the specific hardware present on your mobo. HOWEVER, there is a significant factor to consider. Basically, there is no standard for how RAID is done. So if you run a RAID1 pair using your mobo's BIOS and the mobo craps out so you have to replace it, you cannot be sure the new mobo's RAID system will be able to understand what is on your disks. For this reason, some people prefer the Windows software, assuming (reasonably) that Windows in the future will not lose its ability to deal with older RAID disks of its own making.
There are two ways around this dilemma. RAID1 specifically is better at this than some RAID systems because it is simply identical copies of stuff on two HDD units. Often when a RAID pair has to be moved to another machine or mobo, even if it does not work right away you can "break" the array back into two independent HDD's (simulates a situation similar to recovering from one failed HDD unit) and at least one of them can be used as if it never was a RAID disk.
The other way inspires more confidence. SOME RAID chip makers and the BIOS's involved have given guarantees that they will NOT change the way their chips do RAID from one generation to another. This means that, if you have to replace the mobo, you just need to get a new one that uses a HDD controller chip from that same manufacturer, and it should work just fine. I have actually done this. I liked that feature and bought a mobo that uses an nVidia southbridge chip for a machine I built a few years ago with a RAID1 array, because nVidia gave that assurance on their website. About one year ago the mobo did fail - bad capacitors in the power regulation section. I bought a replacement mobo by a different manufacturer that uses a different southbridge chip, but still by nVidia. When I installed it and turned it on, the machine just booted and ran from that RAID1 array with no difficulty at all! So it worked exactly as promised.
Now, your other question relates to how the RAID array is monitored and error alarmed. Often the CD that comes with a mobo has on it a second user manual besides the manual for the mobo itself. This is the manual for the RAID software system in BIOS. Even if that is not on the mobo's CD, check exactly what southbridge chip the mobo has and go to the chip manufacturer's website and look for a detailed manual on its RAID system in the BIOS. That manual should tell you exactly what you need - how to use it to set up a RAID array, how it will monitor for you, what warning messages it might send out, what built-in tools you can use manually to check the disks in your array, how to recover from a HDD failure, etc. You REALLY should know these things BEFORE you have to fix a broken RAID array. But just to allay your fears, most RAID1 systems handle one HDD failure well. They will send out an alarm to tell you (just don't ignore it!), then fall back to using the remaining good HDD and keep on running. That is the main reason for using RAID1! Then they will have good tools for telling you which HDD has failed, and for re-creating a fully functioning array once you have replaced the bad unit.