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>1 - Amy walks into room after eyepatch lady disappears
She goes into the room to check out the eyepatch lady, who had disappeared by the time she got there. Not the other way around.
>2 - Randomly finds random picture of herself and kid
Implying that it's her child, notice how her hair is messed up and she looks tired in the pic like she's just given birth or something.
>3 - little girl shows up in spacesuit
Well duh, it's her room.
>4- 2 silents show up
Most likely they brought the girl back/followed her back to get their hands on Amy using the girl as a decoy/bait.
They probably lose interest in the girl then as they've got Amy and she can use the opportunity to escape. The Silence could've walked straight out of there somehow cloaking Amy because everyone forgets they've seen them anyway.