Sara advised to go to acting school by her own dad after gaslight

She was very bland in the movie. The only film where she managed to give an exceptional performance so far has been Kedarnath. There the director said everything you see from Sara in this movie is Sushant. She herself stated he helped her from A to Z. He helped her grasp her character to the nuances like pronunciation. 

The only very consistent nepo kid from this generation is Alaya F. She has this very earthy warm appeal in her looks too. I actually do not find Sara that pretty face-wise. 

Sara Ali Khan went to Acting School in US, after shooting for this movie. She was advised by his father to learn how to express and emote better and improve her acting skills for her future Horror movies like Gaslight.

https://www.imdb.com/title/tt27012110/trivia/?ref_=tt_trv_trv

Or she can keep on coasting for 10, 15 yrs like he did and then find one somewhat decent role like Omkara and be hailed as 'so underrated' from then on

Or just quit acting

Why do actors go to acting school in US? Shouldn't they learn it from some Indian institution for better grasp of indan cinema?

An Indian Institution requires a full 4 year degree in acting alongside multiple years of preparation. It is very time consuming. No one in this generation has been able to debut from an Indian Institution under the age of 30 (Zahaan Kapoor, Junaid Khan..etc are big theatre artists and Indian Institution Actors but both are quite old). 

For an actress now that is unthinkable with a shelf life of like 40ish at best to debut at 30. We do have rare cases like Tripti, Aditi and Mrunal seeing fame at an "older age" but the star value has diminished in the public's eyes. 

Sara already has a personal acting coach but a personal coach/formal acting training doesn't always work for everyone. Bobby Deol needed 20+ years with a coach to be an adequate actor.

Some people are spontaneous and do their best acting without guidance. Some people just have "it" but are clueless offstage. 

For example, Alia Bhatt is someone who could learn with a traditional coach. The pros of that is that she improved quite consistently, but the con of that is that she can also regress/forget her acting skills faster if she does not keep up [which is why she keeps an eye on her competitors]. 

Ranveer Singh is someone who is more spontaneous at acting. He can make a mediocre script excellent but he mostly goes off the director's vision. 

One way is not better than the other, but it's safe to say spontaneity is not working out for Sara like it did for Saif or Kareena. The reason why a lot of people debut cold is because the Indian audience tends to significantly prefer spontaneous actors, but that's no excuse to debut with bad skills. 

any examples of somebody who went to acting school and successful?

There is an acting school right in Mumbai that most of the star kids go to anyway. It takes few months to complete. I have visited it and met the teachers. But someone I know with a filmmaking degree stated they hardly know anything about acting. That there is a school in NYC that teaches proper method acting. And most Hollywood directors require their actors to be trained from there. 

I mean to say learning from Indian coach. Not all institute takes 4 years like NSD. Some has courses for a year. Even anupam kher has a coach. They can try doing theatre too for better expression and real time acting. 

I didn't know about actors having personal acting Coach, that's a new news for me.