In RAID 1, mirror, you have one logical drive and everything you write to the logical drive is written to both physical drives. The content of the drives is thus identical.
If one of the physical drives breaks, then you still have same logical drive with same content (in the remaining physical drive). One would replace the broken disk and the RAID would resync content from the ok drive in the background.
Drive is hot-swappable, if the hardware supports hot-swap. However, some disk breaks do report up to OS, which can panic. A restart might be necessary.
With reboot, we get to big question: What kind of RAID 1?
Hardware RAID has dedicated RAID controller and does all the RAID operations within the controller. From OS point of view it “just has a disk”. The mirrors are complete.
Software RAID is all in software and CPU does all the work. Since OS sees the physical drives, it is usually the individual partitions that are mirrored. If legacy mode is still in use, boot starts from sector 0, which are not mirrored. They should thus be written so that boot from the second drive is possible.
Fakeraid is effectively software RAID. Chipset has some tools, but OS and CPU still do all the work.
That gets us to the motherboard. With hardware and software RAIDs all metadata about the RAID array is in the disks, hardware controller or software. Mobo does not matter.
With fakeraid, the chip on new mobo must be compatible with the old mobo. Furthermore, during boot the bootloader loads kernel and initrd-image. The image contains drivers that kernel needs to initialize essential hardware. E.g. to mount the root filesystem. If mobo has different components, then the image probably lacks drivers from them. The image of rescue kernel has all drivers, so it can be used to fix non-booting regular kernel.