Was it fair to bite Shurpanakha's nose by Lakshmana? How?

Shurpanakha was the daughter of Kaikesi and Vishrava Muni (Vishrava and Raka in Ramopakhyan in Mahabharata) and she was not a woman of pleasant looks. Ravana and his family married her off to Vidhytjhivha, son of Kalaka but later in a battle with Kalkeyas, in warrior frenzy he killed Vidhytjhivha. Shurpanakha lamented the death of her husband in front of her brother and he said he couldn't recognise Vidhytjhivha in warrior frenzy and therefore failed to protect him. He gave his sister many gifts and sent her to Dandakarnya to stay with their cousin Khara.

There she saw Shri Ram and got infatuated. She approached him for love but Shri Ram told her that he was married and a woman like her won't accept a co wife so she should approach his half brother Laxmana who didn't have his wife with him in Jungle. She found Laxmana even more handsome and fascinating but he said that he was in service of Shri Ram so she should approach Shri Ram instead of him. Basically the brothers were jesting with her probably thinking that as a princess Shurpanakha would have some dignity and would either leave or say some harsh words to them but dimwit Shurpanakha thought that that they were rejecting her because of Mata Sita who didn't say a single word to Shurpanakha despite her openly lusting her husband. She tried to attack Mata Sita to kill her and then Shri Ram got furious and said one should never jest with idiots and told Laxmana to punish her. Laxmana cut her nose and ears but didn't kill her as she was a woman. She ran to Khara who along with 14000 soldiers attacked Shri Ram but he single handedly annihilated all of them. Then she went to Ravana and told him what happened and ignited his lust for Mata Sita and the rest is history. The fate of Shurpanakha is not known after that but the women of Lanka blamed Shurpanakha for lusting Raghavas and bringing doom on their Kingdom. Not a single person accused Shri Ram for the war because they knew Ravana and Shurpanakha were at the fault.

Source: Valmiki Ramayana

Who was Suparnakha's husband in the Ramayana?

 

Surpanakha and Vidyutjhiva

Surpanakha was married to a Vidhytjhivha, son of Kalaka. After the marriage, Ravana, his brothers and his men went to a forest for celebrations where he met demon Maya and his daughter Mandodari and got married to her when given her hand by her father. Later, during a war with Kalkeyas, Ravana killed Vidyutjhiva which pained Surpanakha. She lamented in front of Ravana who said that he didn't recognise him in warrior fury and failed to save Vidyutjhiva and then he gave some gifts to Surpanakha and sent her to live with Khara in Dandakaranya.

Later Surpanakha fell for the looks of Shri Ram and Laxmana and proposed to them and when her dimwit head couldn't get they were just jesting with her, she thought they were rejecting her due to Mata Sita and therefore tried to kill her and then Shri Ram got angry and told Laxmana to punish her and he cut her nose and ears. She was left alive for being a woman.

Why did Surpanakha's encounter with Rama and Lakshmana lead to such major consequences?

Surpanakha was an unpleasant looking sister of Ravana but in Uttar Kand it's mentioned she could change her form at will. She was widow of Vidyutjhiva, son of Kalaka. Ravana had killed him in a war and she lamented in front of Ravana who to pacify her gave her gifts and sent her away to Dandakaranya to live with Khara, their cousin.

Once when she was roaming around, she saw Shri Ram and was immediately infatuated. She approached him for love but he said he already had a wife and a woman like her wouldn't tolerate a co-wife so she should approach his brother Laxman who didn't bring his wife along. Basically he was harmlessly jesting with her thinking as a princess she would ultimately leave with dignity after rejection. She approached Laxman and he said he was just a servant and she should go back to Shri Ram.

Being a fool she couldn't understand that the Raghavas were only jesting with her and intentionally rejecting her. She thought the brothers were rejecting her due to Mata Sita who didn't say a single word to Surpanakha. She tried to attack Mata Sita to kill her but got saved by Shri Ram. Ram got angry and he said to Laxman that a sensible person must never jest with fools. He ordered him to punish her and Laxman cut her ears and nose but left her alive as she was a woman. She later said that yo Ravana they spared her life as she was a woman.

She complained to Khara who along with Dushana and Trisira took his ogres but Shri Ram single handedly defeated them. So she ran off to Lanka and complained to Ravana who at first was sceptical but when she described beauty of Sita and lied to Ravana that she went to take Sita for him , then Ravana out of his tendency of lusting every beautiful woman in the world decided to abduct her and then the tragic events happened which brought no good to anyone.