How to stop S.M.A.R.T check running for external hard drive?
It depends on your motherboard. Its BIOS may or may not have an option that can help, but you will need to specify what board you have.
Why the check is turn for the external disk?
Again, it depends on the motherboard. Some will exclude external drives (in fact some systems cannot access SMART data on external drives even if they want to).
Is there a way to use the "S.M.A.R.T" check only for my main hard drive?
Why it takes 4 to 5 minutes more, as my both hard drives - internal/external are 1 TB?
This depends on numerous factors. I assume it is connected through USB. This means that when the BIOS POSTs, it has to first initialize the basic systems, then the USB controller, then the drive has to spin up and initialize, then it has to read the drive’s SMART data. This doesn’t usually take too long, but on my system, having any external drives (even a flash drive) adds a good 10-70 seconds to the POST time (I can’t explain the large variance).
Your BIOS may have options to limit the timeouts for the various operations. For example, my board lets me choose who long it will wait for a drive to spin up, for a USB drive to respond, etc. (I usually set it to the minimum of 10 seconds).
There should also be some options that you can set to change the mode that the drive uses which may help speed things up. Also, the drive itself (and the USB enclosure it uses) will have an effect on the initialization and response times.
Once again, it depends on your board.