1. What gotra does westerners belong ?
Gotra system is popular in Hindu community. Over 85% of worlds population do not believe in Hinduism. According to Hindu belief the world is created by Bramha and all people of earth belong to the clan of any one of the mind born sons of Bramha leading the gotra. Then what gotra does other people belong ?
There are some factual solutions for this. Vishnu is all-pervading spirit of the Universe and rests in the heart of all beings. Vishnu belongs to all Gotras. So we can refer anybody who don't know gotra can be refered to "Vishnu gotra".
There is another view too. Maharishi Kashyap is considered the father of the Devs, Asurs, Nags, and all of human beings. So, since he’s the father of all people, if somebody don't know their gotra they can use "Kashyap gotra" as well.
2. When a girl get divorced, what gotra she belong ?
When a girl born she belong to father's gotra. When she gets married she is ritually transferred to husband's gotra. But when the girl gets divorced they usually divorce on social or legal term. There is no any hindu ritual special for divorce. So which gotra the girl belong after divorce, husband's gotra or father's gotra.
The solution is, though divorce is not done on ritual term, after the divorce the girl has no any right and obligation to husband. She even don't wear Sindoor or Pote or Mangalsutra which is the sign of having husband in Hindu culture. She don't use the surname of husband. So the girl goes back to her father's gotra after divorce.
3. Why some people are considered untouchable ?
All of people in this earth belong to one of the rishis. All of these rishis had equal status in terms of social acceptance. If all of the people in earth have same ancestor of same status then why some of the race are considered untouchable ?
Jatipratha or racism is the drawback of hindu society. It was actually created by some of the creepy minded people to keep their dominance on the society. Innocent people followed those rules and it developed as tradition. We should stop these bad stuffs of hindu culture. Everybody is equal in the eyes of god.
4. Is it ok to merry the person from same gotra?
This is one of the prime debate in Hindu community. Almost all communities and religions its unacceptable to merry your own family members or somebody your related by blood. Same gotra technically means people having same ancestors. So the answer absolutely depends on how you define gotra and family.
On legal term in Nepal its ok to merry any body who does not belong to your family up to 7 generations AND who is at least 18 years old. So if anybody qualifies on these two basic requirements you can merry them even if you belong to same gotra.
One the other hand, on social perception it will still be considered unethical.
As per scientific perception, if the gotra is perfectly identified and people belong to the exact same gotra what they claim for, the babies born from the pair of different gotra has more chance to be healthier than that of same gotra.
List of Gotra and Thari
List of Gotra and Thari