Is partial rooting possible?

So I was a jack*ss and let my brother's friend use my phone then I crashed out of exhaustion from an insane day. Hours later I wake up and take my phone back. Everything was completely different. I pretty much couldn't use it for anything but texts and calls.

I found out by taking it in that it had been rooted. Slowly I learned how to use my phone again, operate on cyanogenmod, some of the perks and other things I knew nothing about. But the thing is, as I learned more I realized it definitely isn't rooted properly or completely. (I'm far from a pro but I'm trying to get closer to it) so

*I did several root checker apps some said I was rooted some said I wasn't

* None of my apps can gain root access. If the option is available, I try and no go.

* None of the super use apps I've tried will work.

*I can see and do somethings I wouldn't be able to if the phone wasn't rooted.

I have es task manager and file explorer so I can see residual files that would come from rooting so I'm confused. What's my phones real root status? Can I wipe the old improper root job, and residual apks/files so I can root it correctly?

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Is partial rooting possible?