If I want to select the BIOS configuration or the boot menu, the computer does either not react on pressing the F2 or F10 button or it resets and at the second try it reacts as expected. This can't be the usual way. I had many mainboards before and no one shows such a behavior. I think this is a BIOS bug. If I press F2 as it is shown on the lower right I expect to go in BIOS configuration and not doing a reset, same for F10.
I see that you are having problems during boot with your Intel(R) motherboard.
First I will like you to confirm the motherboard model number and the BIOS version that you are using as this may be a BIOS corruption.
If you are not using the latest BIOS, I recommend you to perform an update and load the BIOS defaults with F9.