1 and 2 are grammatically correct, but they do not mean the same thing.
1 means she is holding the glasses in her hand.
2 means she is wearing the glasses so that her eyes can look through them and what she sees will be clear instead of blurry.
3. Who is the girl with glasses?
(Does #3 mean #1 or #2?)
It could mean either 1 or 2, but I would take it as meaning the same as 2.
From public dot wsu dot edu,
When you mean “for example,” use e.g. It is an abbreviation for the Latin phrase exempli gratia. When you mean “that is,” use “i.e.” It is an abbreviation for the Latin phrase id est. Either can be used to clarify a preceding statement, the first by example, the second by restating the idea more clearly or expanding upon it. Because these uses are so similar, the two abbreviations are easily confused. If you just stick with good old English “for example” and “that is” you won’t give anyone a chance to sneer at you. If you insist on using the abbreviation, perhaps “example given” will remind you to use “e.g.,” while “in effect” suggests “i.e.”
Since e.g. indicates a partial list, it is redundant to add “etc.” at the end of a list introduced by this abbreviation.
They are both examples.