I never said the bios was "dependent" on the OS. I said it was "independent" of the OS, which means, one should not affect the other, at all, except that a newer OS is likely to run better if you have the most recent bios version installed. Do not rely on an automatic utility to make this determination for you. Verify your bios version against the latest available bios version yourself, visually, with your own two eyes. The automatic utilities will often tell you that there is no newer bios version available when in fact there is one, or even several.
You do not need to install each version that is newer than yours, if there are any. Each bios version supercedes ALL previous versions so if you have, for example, version 1234 and there is a version 2345 and version 3456, you would ONLY need to install version 3456, not version 2345. You can find the bios images on the product page for your motherboard model.
Intel management engine interface is not necessary (Although it's highly recommended for the operating system) in order to install newer bios versions manually, via flash drive. There are instructions on flashing the bios manually on the product pages of every modern aftermarket motherboard.
Are you having problems that lead you to believe you need to update the bios or that there is a newer bios version available which you would like to install even if you are not currently having issues? What is your operating system version?