Toilet keeps running, also what type of toilet is this?

[DaluTulak]

Hi, I fix what I can around the house myself and have fixed a few toilets but I need help with this one.

This toilet keeps running and stopping, running and stopping, etc. I've cleaned the rubber flapper itself and at the point that it contacts the reservoir, so I don't think it's leaking from there and I've watched all the korky fill valve videos, nada. Any help would be amazing!

Also, can someone explain to me why the previous owner stuck the fill tube into an actual tube and stuck it in that hole? What does that hole do? I don't want to mess with something I didn't set up to begin with. There are also holes in the back of the toilet that allows the water to overflow behind the toilet?

Any and all help is appreciated but please keep in mind that I don't know all the plumbing lingo.

I attached multiple pictures as well.

Thanks in advanced!

 

[Rtplumb]

Hi, could you post a picture of the whole WC, pan and cistern.