Are there any strange demands of Bollywood actresses?

 Kareena Kapoor Khan

One of her demands is that she won't work with 'B' grade actors. Hence, the actress is only paired with A-listers on-screen. Kareena has an infamous reputation of having rejected quite a few films that were offered to her and the reason seems to be her reluctance to work with anyone else than A-listers.

Sonakshi Sinha

Sonakshi Sinha comes with 'no kissing on-screen' clause. The actress is very strict about her clause of not kissing on screen. She has not been a part of any kissing scene so far and it remains to be seen if she will ever break the clause.

Deepika Padukone

Deepika Padukone refused to share the screen space with one of the most versatile budding stars Vicky Kaushal who did an extraordinary job on screen in 'Masaan' and 'Raman Raghav 2.0'. He was supposed to play a crucial role in Sanjay Leela Bhansali's 'Padmavati', but since Deepika wouldn't share the screen space with him, he had to be thrown out of the project.

Kangana Ranaut

The actor comes up with an utterly-bizarre demand. She never speaks for herself. Instead, her personal assistant always answers all the questions and queries without involving Kangana. Also, she makes sure that her personal assistant always travels with her.

Aishwarya Rai Bachchan

It is said that while flying, she keeps the flight attendants on their toes. She asks them to present before her, all the dishes available one by one. She then selects the most visually appealing ones!

What are some examples of actresses who became directors after feeling limited as an actress?

 One of the finest example of this will be Aparna Sen and Nandita Das.

Aparna Sen started her career as an actress and worked in Bengali and some Hindi films. It was during the film Imaan Dharam that she felt that she was reduced to useless decorative roles in big commercial films. Shashi Kapoor played her brother in the film who was starting his own production house at that time to make his kind of films- artsy, meaningful cinema. Aparna Sen narrated her script to him and he was more than ready to produce it given that his wife Jennifer Kendel plays the lead role. And thus started the career of Aparna Sen as a director with 36 Chowringee Lane, which won 3 National Awards including Best Director and Best Feature film in English for Aparna Sen. Till now she has won 9 National awards and has made path breaking films as director in English, Bengali and Hindi. Some of her remarkable movies include Paroma (2 National awards), Paromitar Ek Din (3 National awards), Mr and Mrs Iyer (4 National awards) etc.

Similarly se have Nandita Das, an actress who is in the industry for more than 4 decades but haven't really got the kind of work and appreciation that her talent deserves. She was also the one to raise the question of racism and discrimination against dark skinned actors in the industry. And she expanded her horizon by turning to filmmaking. She started off with documentaries and public service advertisement and then made her first feature film Firaaq. The film won 5 Filmfare and 2 National awards. She has made critically acclaimed films like Manto and Zwigato as well. She as worked as an actor and director in plays, given her voice for audio books, been a chair of Children Film federation etc apart from her acting roles.

Why did actresses like Babita and Neetu Singh stop acting after marriage, and how has this trend shifted in modern Bollywood?

 Because of the patriarchal setup. According to the tradition of the Kapoor family, the women of the family are not supposed to work in films. So both Babita and Neetu Singh had to stop acting after their marriage.

Raj Kapoor also believed that filmy bahus don't make good traditional housewives, so he was very much against the marriage of his son to actresses. But Randhir Kapoor and Rishi Kapoor managed to marry with girls of their own choice. But Raj Kapoor put his foot down for the third son Rajeev Kapoor who was not allowed to pursue actresses Padmini Kolhapure and Divya Rana. Raj Kapoor even threatened Padmini to throw her out of Prem Rog if the romance continued. Rajiv Kapoor blamed his father for his personal and professional debacles. Shashi Kapoor’s daughter and wife also worked in films and he produced his wife's film 36 Chowringee Lane, but refused to launch his children. Shammi Kapoor's wife also left films after marriage.

This trend changed with Karishma Kapoor. Babita was a highly ambitious lady and she wanted to see her daughters successful. Also the career of Randhir Kapoor remained patchy due to which they needed financial stability. So Babita at the risk of tainting her marriage with Randhir groomed Karishma to become an actress, and she became the first daughter of Kapoor Khandan to work as an actress. This was followed by Kareena Kapoor and their success opened the gateway for women working in the films. Even Neetu Kapoor made her comeback in 2009 and since then has been working on limited projects. Now even the daughter of Neetu Kapoor, Riddhima has made her debut with her mother in Dadi ki Shadi. And Alia Bhatt is an established actress already.

This tradition was common in many Bollywood families wherein actresses left movies after marriage. Amitabh asked Jaya to stop working in films after marriage at the time when she was at the peak of her career. She returned occasionally to films but sacrificed her larger career. Dilip Kumar wanted Madhubala to leave movies after marriage and the relation couldn't sustain. Sunil Dutt was adamant that no women of her family should work in films. So Nargis Dutt left movies after marriage even though she was perhaps a bigger star than Sunil Dutt at that moment. She only returned to do one film for her brother and won a National award for that. And Sanjay Dutt continued this tradition of not allowing his wives (Richa Sharma and Manyata) to work in films and even when his daughter Trishala wanted to work in films he didn't let her.

What are the lists of some actresses which have simple personality in South Indian film industry?

 Keerthy Suresh(most simple one according to me)

Kajal Agarwal

Sai Pallavi

Rashmika Mandanna

Rakul Preet Singh

Anupama parameswaram

Sree Leela

Who are the talented but underrated actresses in Bollywood?

 There are quite many Talented yet Underrated Actresses in B'wood. But Some of the more prominent ones are:-

Konkana Sen Sharma

2. Tabu

3. Nandita Das

4. Tisca Chopra

5. Richa Chadda

6. Divya Dutta

7. Radhika Apte

8. Swara Bhaskar

9. Kirti Kulhari

10. Sayani Gupta

11. Kalki Koechlin

12. Shweta Tripathi

Edit:-

Tillotama Shome and Rasika Duggal for Qissa

Tanishtha Mukherjee

Surveen Chawla for Parched and Ugly

Edit 2:-

For those who're saying that 'These Actresses aren't Underrated because they've Won National Award'. This Argument is wrong! Just because they've Won National Award, doesn't means that they're Treated at par with other ‘Mainstream A Listed Actresses'. Underrated, here means that they don't get same attention from Media, Mainstream Award Shows and Big Production Houses. These Actresses usually don't get Same roles as Deepika Padukone or Kareena Kapoor.

Edit 3:-

Sorry for this late addition here but lately I remembered her, so thought to list her.

Nimrat Kaur (Honoury Mention)

Though some might think and start sayin that 'she's not underrrated' et cetera et cetera but I believe that she indeed is an Underrated Actress. After proving her Metal again and again, Even Hollywood gave her big projects and yet Our Nepotism filled industry (Bollywood) is still not Casting her in Women Centric and Strong Protagonist Roles.

Which Bollywood actress had a very short career span and then disappeared?

 A lot of names have already been mentioned in other answers. So, I will try to add a few more names which have been missed.

Gracy Singh : The graceful and beautiful actress from Lagaan, seems you have disappeared. She acted in few more movies but she is not seen making any presence on-screen since quite a few years.

Anita Raj : She did good nunber of movies and was popular too but she disappeared after those movies. She made a comeback on small screen.

Amrita Arora : Not that she had amazing acting skills or anything but she tried for few years but now she has almost disappeared.

Koena Mitra : TThere was a phase when her presence could be felt very much on-screen. But, gradually she disappeared. She had acted in movies like Apna Sapna Money Money.

Payal Rohtagi : She had made numerous controversial statements and I believe she still does that. However, she seems to have disappeared from the big screen.

Yukta Mukhee : The beautiful actress had started in few movies but she could not make it big.

Diana Hayden : Another beautiful lady who had no luck in Bollywood and disappeared from Bollywood.

Trisha Krishnan : She is a popular name in the south movie industry bit disappeared from Bollywood after doing Khatta Meetha.

Kajal Agarwal : Another popular name from south movie industry who appeared in the Hindi movie Singham and then disappeared.

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