1. Mangni: This is the engagement ceremony, it's not actually called sagaai haha like they keep saying in the show.
2. Prayers: A prayer ceremony is usually conducted to kick off the wedding rituals, to pray for the happiness of the bride and groom. Much like a pooja conducted in Hindu weddings.
3. Mehendi: I guess this is pretty self explanatory haha.
4. Nikaah: So this is the main thing, the bride, groom, their respective fathers, as well as two other representatives from each side (called Walis which means witnesses) are involved.
5. Meher: As part of the Nikaah, a certain amount of money or gift is given to the bride by the groom. Two members of the groom's party go to the place where the bride is sitting and present it to her, and the bride's family reciprocates with gifts to the two persons.
6. Ruksati: This is just the bidaai of the bride, she bids farewell to everyone and is then brought to her husband's house by her brother.
7. Walima: This is just an equivalent of a wedding reception held after the Nikaah in celebration of it.
Okay so at least that's what happened in my sister's wedding, I still don't know what's a rasame saugat or whatever haha. But as far as I know, basically for a wedding to be considered valid, just the Nikaah has to be done, the rest of the rituals are not exactly compulsory.
Hope this helped (: