Developer Options is just a link in the Settings menu that's typically hidden (... it needs to be intentionally revealed by the user).
Whether there is or isn't a problem with your phone to display the Developers Options menu has nothing to do with your problem, Rooting your device requires you to download and use third-party utilities on an installed Android OS, the exposing a base Android Developers Options menu is irrelevant.
So either focus on rooting your phone or on revealing the Dev. Ops. menu, but working on both at the same time is just creating unneeded confusion. And more the to point, I doubt rooting your phone will be a fix your stated problems anyway. Just how do you think so? Rooting is not some sort of magic fix.
Rooting gives you the ability to do more things to the system-level directories that a typical user is restricted from, but it doesn't not give you the knowledge. Tweak a file the wrong way or alter/delete a required folder can soft-brick a phone, requiring you to re-flash the appropriate, stock firmware to restore the phone back to working condition. Approach rooting your phone to accomplish a specific task, don't just do to unknowingly experiment.
Of course if that's what you do want to do, rooting is good way to educate yourself on how your phone's Android OS works in the background. This being a dated model running Nougat is this just a spare secondary phone or your daily usage phone? Experiment with a spare,, not with your primary.