[mws_1984]

I usually keep my phone muted and on vibrate. But sometimes after having it plugged in to charge and I go to access it, the sound has come back on without my touching it.

Another one I will have set an alarm but sometimes I wake before it and I shut it off. But the alarm has still gone off despite my turning it off before the scheduled wake time.

[Ariel Babalao]

Really odd actually. But unless the physical mute on/off button is defective, or you switch it on without knowing it, or you install an application to over write the physical mute on/off button, say from Cydia for example there is no way that the phone will auto on off mute/vibration.
I would suggest you to do a back of your files to iCloud and factory reset the iPhone.

The same goes to the alarm wake up, probably there is another app that's also set up to go off at the same hours even though you turn off one, the other still goes off, or there is another tweak force overwriting the alarm to stay on even though you turn it off.
Factory restore it to solve it, if your iPhone is not jailbroken.
You can later on restore you backup after factory reset.

[mws_1984]

Really odd actually. But unless the physical mute on/off button is defective, or you switch it on without knowing it, or you install an application to over write the physical mute on/off button, say from Cydia for example there is no way that the phone will auto on off mute/vibration.
I would suggest you to do a back of your files to iCloud and factory reset the iPhone.

The same goes to the alarm wake up, probably there is another app that's also set up to go off at the same hours even though you turn off one, the other still goes off, or there is another tweak force overwriting the alarm to stay on even though you turn it off.
Factory restore it to solve it, if your iPhone is not jailbroken.
You can later on restore you backup after factory reset.

Only happens every so often so its not a big deal. My phone is in a lifeproof case so its annoying trying to toggle the mute/unmute so I use the triple click of the home screen to access the sound controls. And I access the alarm clock the normal way.

[Ariel Babalao]

Ah ok, I do not know much about accessibility in iPhone and how to deal with misbehaving settings of accessibility. I can only think that perhaps you toggle it on without knowing it? Hopefully someone with a better knowledge on accessibility can advice how to cure that odd behavior.
As for the alarm app, it's also odd if that's the only app you using. Have you tried killing the app from multitasking and performing a hard reset? Home+power buttons press down until iPhone turn off and comes back with apple logo, then you release both buttons.
Which which iOS is it?