if every single hardware device or item of a PC-System, like hard-disk or cd/dvd-rom drive or pci-card or floppy, has an own little bios-chip,
Not exactly. What those devices will have is a microcontroller or an ASIC that is programmed to do the work. It's not a BIOS per say but it is code. Most of the time its not user accessible unless you happen to know some special things about the device.
the ques is, for example, if PC beginner simply plug off such a device, while PC is switched on, and "damage" this device, that probably this device is not damaged, cause you only need to re-flash this little BIOS-chip or hardware-TM-brand-chip of concerning device ???
Nope. Most of your failures are from manufacturing flaws in the solder reflow process. A joint that is not completely soldered will over time fail and cease to conduct or conduct so little that the device no longer works. The reason this happens on power on/off most of the time is thermal expansion. Every time a device is powered on or off the joint goes through a thermal cycle. A bad joint only has N cycles before its no good. So when thermal cycles > N the device fails or starts doing flaky things. I'd guess in most cases the higher resistance of the joint causes a slight shift in the timing of a signal and the device starts doing flaky stuff.
Its really hard to find these joints in a manufacturing line. In a lot of cases the flaws are only evident via X-Ray of the joint. Current cost margins for devices do not allow the Mfg to 100% X-Ray inspect all the boards. So they work for a bit and get the process tuned out until the process line yields a set of boards with a % defect rate that's below what some exec or marketing person had deemed acceptable.
Then they just start cranking out parts with spot checks here and there.
In most cases these flaws will pass the "test" and "burn in" phases with no problems since the N level may equate to a week or so of use. Some times the temperature extremes and shock its exposed to in shipping will be enough to push it over the edge.
When a device does have flashable firmware and the Mfg provides an upgrade to "Fix" some issues a lot of those cases are where they have enough field failures to identify where the timing is "marginal" and apply better software to compensate. In the case of devices with an FPGA in them they can directly change the timing by adding buffers or latches.
Hope this helps.