When chalazion require surgery? Please help. (photos)

Thank you for sharing your concerns. Unfortunately, styes frequently reform after the seem to resolve. There is no reason to put your daughter through surgery with general anesthesia at this point. Kenelog should be injected into the lesion and it should resolve. Whether it disappears with the injection or incision and drainage it could still return in the future. Daily eyelid washing and warm compresses can help keep it at bay. Good luck. 

Especially on the lid margin, I personally think that surgery should be a last resort.  Almost all of these lesions can be treated with a steroid injection with Kenalog.  In the past 20 years, I have not had a single stye that did not respond to this treatment.  Unfortuately surgeons make much more money doing surgery.  In my opinion your daughter is being over treated for these.  I am concerned that her eyelids will be permanently scared by surgery she does not need.

It probably should be drained since the stye/chalazion has been there for this amount of time. (FYI Chalazion refers to a nonresolving stye.)

If a chalazion is not gone after warm compresses in 1 month it generally needs to be excised. In short, antibiotics don't help chalazion because it is not an infection.  I have a website dedicated to chalazion and styes called denverstye.com. You can read about treatment, when to have surgery etc..- Dr T