Two difficult phrases

[Theseus]

A young lady wants to impress a rich high society woman,who is surrounded by a large circle of friends & who is interested in art & fashion. The first sentence is this:

Για χάρη της πήρα την απόφαση να δώσω τις φωτογραφίες μου στην έκθεση της γκαλερί «Παντιά». Δεν τη θεωρώ χαζή, όχι!

What does the bit in bold mean: "At her exhibition"? What on earth is the grammar of γκαλερί «Παντιά»? Does it mean "at the gallery Pantia"? Why not στο γκαλερί? Does "Pantia" mean anything?
The second is when the young lady in question meets this woman at a fashion show:

σε μια επίδειξη μόδας. Καθόταν στην πρώτη σειρά και κοιτούσε δεξιά και αριστερά. Η μελαγχολία της μ' έκανε να θέλω να κλάψω και να γελάσω μαζί.

Who/what does the μελαγχολία refer to? The society woman or the fashion show? I presume the former but there is no mention before that she was depressed.
I probably am tired & unable to find an obvious meaning at first reading. That is why I need some help. The textbook I have been following has suddenly got harder & I am getting somewhat frustrated.:down::curse:

 

[SBE]

Στην έκθεση της γκαλερί Παντιά means at the exhibition of the Pantia gallery.
At her exhibition would have been στην έκθεσή της, note the accents.

Η γκαλερί (feminine noun): a gallery, an art exhibition space.

Παντιάς= name and surname, a contraction of Παντελής

Για χάρη της πήρα την απόφαση να δώσω τις φωτογραφίες μου στην έκθεση της γκαλερί «Παντιά». Δεν τη θεωρώ χαζή, όχι!

Thanks to her I decided to submit my photographs to the exhibition at the Pantia gallery. I don't think she is silly, not at all. (obviously she thinks that the other woman has advised her well about the photos)

 

[SBE]

Regarding the other query:

Καθόταν στην πρώτη σειρά και κοιτούσε δεξιά και αριστερά. Η μελαγχολία της μ' έκανε να θέλω να κλάψω και να γελάσω μαζί.

She was sitting at the front row and was looking right and left. Her sadness made me want to cry and laugh at the same time.

Η μελαγχολία της refers to the previous sentence. If the writer wanted to refer to the show then she would have said: Η μελαγχολία της επίδειξης (μόδας) μ' έκανε να θέλω να κλάψω και να γελάσω μαζί.
But putting these two sentences side by side would be a logical leap. She is discussing the woman in the front row, why jump to her own feelings about the show like that?

 

[Theseus]

SBE, thanks so much. I had wrongly assumed γκαλερί was a neuter noun. Thanks to you, the sense is now quite clear. 'Pantias' I could never have guessed. As to the second part of the enquiry, I felt that a fashion show could hardly have the noun μελαγχολία applied to it but you have explained everything so lucidly. As I said, I work so hard at my Greek that I get tired & fail (in this case, lamentably) to grasp the obvious meaning. I thank you too for your detailed notes.:blush::)