Omkara and Gauri: The Mythological symbolism
Omkara represents that version of Shiva, which is meditating on Kailash, in pursuit of truth. Om', the word itself represents the universal truth, therefore the Omkara form of Shiva, is the Bairaag/Tapasvi form of Shiva, who has renounced the world, and is meditating in seclusion to find the universal truth. This is the form of Shiva with long, uncombed hair and tattered clothes (which is why our Omkie also has long hair and doesn't care two hoots about fashion sense)
As the story goes, Parvati was smitten by Shiva and wanted to impress him. Here there are two branches of the story. In the first version, she asks a boon from Brahma to make her pretty and fair, so that she can impress Shiva, and he grants her that boon in the form of Gauri. In the other version of the story, Parvati undertakes a difficult journey to reach Shiva, during which she is covered with dirt and in ragged condition. So, after she reaches Kailash, Brahma tells her to take bath in a holy lake. She does so, and the form that appears from the lake is Gauri, who so fair that she shines like gold. Gauri is the version of Parvati that emerged to please, to impress Shiva. (That's the reason behind her devotion and why she is always trying to please Omkara)
Gauri: The Chulbul Pandey of Bareilly
Gauri is that version of Ma Parvati, who represents good fortune, joy, fertility, devotion, and protecting the weak ones. Also, Gauri ma loves sweets. (Case in point our Gauri loves her kampat', whereas Omkara doesn't like sweet because hey, truth is bitter)
Fate hasn't been kind to Gauri, yet it is not in her nature to blame fate or god for everything. Instead, she has always thanked God for the little mercies he has shown her. Her ShankarJi is her biggest confidante and friend, as well as her protector.
So, we have a Gauri who always stays happy, despite the fact that she is an orphan, fatherless, and mistreated by her uncle and aunt. She stays happy and spreads joy. She is dramatic because her idol Salman khan is larger than life personality. People from small towns are often more taken in by the movies than people from urban areas. His larger than life persona has influenced her too, that's why the antics with candies and shades. She also lies about small things because clearly Salman also doesn't have a problem with it (remember how he didn't care how he got Sonakshi in the movie Dabanng?) So, she likes the drama (remember the Dhrurindhar incident where she created a whole story about car and gifat'?)
When Omkara entered her life
Gauri might be just 5th pass, but she is an open mind, she keeps on receiving knowledge, courtesy her internet chaachi (remember how she learnt about hologram?) When confronted with Kaali Thakur, she didn't break down and give up, she used her brains and fought back. She pretended, lied, danced, and basically made a pappu out of KT. Unfortunately, she soiled her image in front of Omkara. Despite the fact that wasn't keen on meeting him ever again in her life, when Omkara fell unconscious in the jungle, she helped him, at risk to her own life she took him to the Dargah and saved his life. Of course, Omkie did not know that, so he left her to die there (Shrenu's expressions in that scene were epic!).
Her Marriage?
Despite everything, Omkara saved her from the villagers later, by marrying her. Now here there is an important trait about Gauri. She was running from the villagers, and that time her only hope was Shankarji, and she was somewhere confident that her Shankarji would save her. That's when Om came into picture and saved her.
Now no doubt, she would have been devoted to her husband, but she is devoted to Omkara because of a bigger reason. Not because he married her, not because he saved her life, Gauri believes that Shankarji has chosen Om to save her, Shankar ji sent him into her life, that's why she has accepted ShankarJi's decision of her fate. Which is why she OTT devoted to Om, because she believes that's what her ShankarJi wants of her.
Gauri is a mass of contrasts. On one hand, she has accepted Om like Meera, but he has not accepted her, so she will never impose herself on him. She is a girl of the world and a practical girl, so she would never live in a relation that is a farce.
Gauri : Saam Daam Dand Bhed'
This is a Chanakya philosophy, which says that to get a work accomplished a person, can try to explain, buy, punish, or exploit secrets, i.e. basically try every means available but use this method only for good. If Gauri was born in ancient period, then she would have an ideal queen who uses every means possible to achieve her goal.
Gauri disguised as Chulbul to get a job, and then backstabbed Svetlana to help Om. She foiled Baumaa's plans by lying about pregnancy. She made a pappu out of Kali, and when need be she stabbed him to escape from him. Like Krishna said that means justify ends, which is why resorting to shady means during Mahabharat, Gauri also believes in the same.
Gauri Kumari Sharma is brave and cunning; she would have made a perfect queen in another era.
Gauri: the Indomitable
Not just villains, Om, even circumstances could not defeat her. Her coming back again and again was not a defeat of her self-respect; it was a victory of her humanity and saving the one person who Shankar Ji had chosen for her.
Om could not break her spirit. He misbehaved with her, insulted her, refused to answer the questions she was asking, confused her with his kindness, but she didn't back down. She came back to save him despite his wishes, and she left him the moment he made it clear that she has no place in his life. Gauri Kumari Sharma lives life on her own terms. She is not a regressive character; she might need a dupatta when she wore gym attire (remember perspiration?) but she totally donned the sari like a diva to help Om get back his inspiration' (many urban girls would still be unable to pull this off).
Gauri cannot be defeated by the name of a medicine, the same way Svet's science experiments could not defeat her, cos she's a modern girl, she is inquisitive and always open to knowledge.
Gauri Kumari Sarma is a survivor
Gauri as survived the worst among all the characters yet she keep herself happy. She will eat chana like a boss, and not cry over the loss of a man who did not want her.
She is the modern girl, who is practical and wants security of her position in someone's life, but not impose herself on him.
At her core, despite all her bravado and cunning, she is simple girl. She led a simple life making clothes for idols and taking care of her mother. She wanted a husband who would cherish her and respect her. She isn't looking for romantic love and ishq, just some appreciation of her existence. But like Gauri said, "Hum jo chahe, uska milna zaroori kaha hai (remember first episode convo with Anika?)
Ab complicated pati mil gaya toh kya kar sakte hain! GKS is a queen, if she has passed all her examinations till now, she'll pass this one too.
P.S: This is an addition to the original post. GKS has long been bashed for being 'regressive' but in actuality she's a strong female lead. She has demonstrated her wits and strength in dire situations. She has used her brain and brawn to save not only her own skin but also of Omkara and his family innumerable times. Also, Gauri is one of the rare female leads who has embraced her sexuality, unlike the shrinking violets we still encounter on television. Doing martial arts isn't the only marker of a 'feminist' lead, standing up for your rights is.