If they are not fast enough to open the circuit there should be damages to the other parts. At least that's what I thought. Am I wrong?
btw can anyone point out a thorough hole fuse that should be a good idea to put in this kind of circuit?
It depends on how the circuit is designed, but what I described above would protect at least the MCU (and likely everything) from almost any lab-accident misconnection. Lightning strikes might be pushing it. Fuses from reasonable manufacturers all have detailed specifications on fusing energy, time-to-blow at specific overloads, etc.
https://www.mouser.com/datasheet/2/240/Littelfuse_Fuse_370_Datasheet_pdf-357362.pdfThe 12V power supply is fine, but if you're going for six AA cells, you might want to consider a low drop-out regulator and Schottky diode, or use eight AA cells. The LM7805 will stop regulating, when the voltage falls below 7V, plus 0.6V for the diode, giving a minimum voltage of 7.6/6 = 1.27V per cell, at which point alkaline cells still have a fair amount of energy left and it won't work very well with rechargeable batteries, which are 1.2V. With a low drop-out regulator and a Schottky diode, it will work down to 6V, giving a longer battery life and compatibility with rechargeable batteries.
I completely agree with using something like the LM2940 if he is using a battery pack, but it is worth pointing out that the behavior of an LM7805 as the input voltage drops isn't that it completely stops working, but rather it becomes less and less effective at filtering, which becomes less important with a battery since there's no input ripple. It also will have the effective output impedance go up, so load regulation goes away too. But the output voltage doesn't start dropping until quite a bit lower than 7 volts if the current is as low as this project is likely to be, less than 200mA. The exact performance will vary a bit from example to example and brand to brand.