Don't put her down.. If she is going to go ............. well them let nature take its course. It appears that whatever she has is not contageous. If it is, then it is too late anyways. Eliminating her now would solve nothing.. If she is eating, then she is living... Just like humans, NOT ALL GROW UP TO BE 100% HEALTHY. We do our best to prolong all life. Chickens likewise can be born with deficiencies.. I am suggesting to let her be and just take the most reasonable route.
WISHING YOU BEST. Keep us updated as she keeps making her efforts to live..
She looks a whole lot like an OEG Bantam (or more likely a cross, full blooded have smoother bodies and long fan like tail). If she is then she is likely an extremely smart and potentially friendly little bird. The OEG Bantams were bred for beauty and brains (show birds) so they are truly a joy, they also make phenomenal broody hens.
It doesn't sound like Mareks to me.
Where did the chicks come from? Is it possible they had a bantam rooster running around with some standard hens?
FYI here is a pic of one of my hens for comparison, she is about the size of a large pigeon: