Michonne turns around in the room and sees another girl (presumably the one in the picture) with the back of her head blown out in a rocking chair

 

The implication is that she killed them and then killed herself. They only show her from the waist up, so the gun could have easily fallen on the floor after she shot herself.

 

What Neuro said. Due to the exit wound of the bullet at the back of the head I would say suicide

 

Yeah. It was either suicide, or someone was really pissed at her so they made her sit down and put the gun in her mouth. But my money is on suicide.

 

Right, even if they had shown the floor around her [they didn't], and there was no gun, I would still say suicide, because a family member could have easily come home after that, found them, and taken the gun for protection.

 

With the way everyone was laid out on the beds so neatly with some of their things in their hands, it most likely was a mass suicide.

 

True. Or if we want to be really depressing, they took the gun and ran away to commit suicide elsewhere. Would make sense. Unless the one who committed suicide went through all the trouble of putting the painting outside that door and then somehow closing it behind herself. Had to be someone else. And it would explain why she didn't pick up the gun. Admittedly, she's very in love with her katana, but I doubt she'd just leave a gun there. Even if she just planned to give it to Rick or Carl.

 

I'm not sure there is a connection between this house and Terminus. The picture seemed to be of a younger girl. I think they just both had similar hair.

 

There has to be a connection. They didn't show that picture of Mary for nothing, or the sunflowers. It was a TWD easter egg for us to find. Maybe Mary is the one that killed them.

 

I'm now thinking that Mary was the aunt of that family, and she killed them all before leaving for Terminus.

It also wouldn't surprise me if Mary is the actual leader of the Termites. Gareth acts like a know-it-all, but it could be a façade.

 

Well, if you call the painting 'Mary', then we are begging the question of whether there is a connection lol. I'm not convinced it was Mary. The painting looks to be a much younger girl, and with the wrong eye color. There were also pictures of flowers and rabbits, and the house can't be connected to everything, so they may have just placed these pictures here for astute viewers to point out all the plot points in the various paintings. But as for the plot itself, I don't think its implied that Mary actually came from the house.

 

Hmm, I didn't notice the eye color, you are good. I still think it's connected. maybe we will find out, maybe not.