Can my wife take legal action for school retaining documents and unethical practices?

The facts posted are too disjointed. Except for the alleged discrimination against the defaulting student, none of the incidents constitute a cause of action.

if she is aggrieved by the behavioral attitude of the school management then she can very well initiate legal action by first issung a legal notice to the school authorities demanding her certificates and also to permit her  withdraw her resignation letter which was forced on her and to allow her to continue her job.

If the school management is not entertaining or complying with her demands then she can approach court for the relief and remedy  

You have raised a series  of issues.

My wife is a teacher at a private school in Delhi. Upon joining the school, they mentioned in the appointment letter that a three-month security deposit was required, and verbally, they stated that she would not be allowed to resign during the academic session.

MANY EMPLOYERS DO SO.  BUT YOU HAVE TO CHECK WITH CONCERNED DD(EDUCATION) OFFICE OF THE DISTRICT AS TO WHETHER THE SCHOOLS RECOGNIZED IN DELHI ARE PERMITTED TO DO SO. 

IF NECESSARY CAN ALSO ASK SUCH INFORMATION UNDER RTI ACT

Additionally, they retained her original documents until the security deposit was paid.

YOU ARE ABSOLUTELY SILENT AS TO WHETHER ORIGINALS ARE TAKEN BACK OF NOT.

Despite these terms, she joined the school. During her employment, the school instructed her to collect fines, trip fees, and annual function fees from students. When one parent did not submit the annual function fee, the school directed her to lower the student's marks, intending to pressure the parent. They also insisted that she should ensure the school's name was not involved in the issue.

SHE HAS PROBABLY DECLINED TO COMMIT A NON-BAILABLE CRIMINAL ACTION.

These demands conflicted with her professional ethics, and as a result, she experienced significant mental stress. On 21-09-2024, she developed a fever, and the doctor advised her to rest, issuing a medical certificate for 10 days (from 21-09-2024). Despite this, she continued working until 24-09-2024 to complete paper checking and prepare results, as her fever was minimal at that time. However, after 24-09-2024, her condition worsened, and she requested leave from the school. The administration dismissed her request, suggesting she take medication and return to work. On 25-09-2024, I accompanied her to the school to submit the medical certificate. During this visit, I confronted them about their unprofessional practices, which were creating unbearable working conditions for teachers. They accepted the medical certificate and allowed her to leave. She recovered from the fever by 04-10-2024, and the doctor issued her a fitness certificate to return to work on 05-10-2024. However, when she attempted to rejoin, the school informed her that a committee, consisting of medical and legal personnel along with school members, would evaluate the validity of her medical certificate. They argued that since she had worked from 21-09-2024 to 24-09-2024 despite being advised bed rest, her certificate was invalid.

SUCH VERIFICATIPN OF CERTIFICATE WAS VALID ONLY DURING BRIEF PERIOD OF HER LEAVE.

They implied that this could lead to her termination.

TERMINATION खालाजी का बाड़ा नहीं है. IT IS APPEALABLE BEFORE DEPTT  AND LITIGATION CAN BE FILED IN DELHI EDUCATIPON TRIBUNAL (at Timarpur)

I Under this pressure and fearing the consequences on her career, they suggested she resign, which she did in haste to avoid termination. We seek legal advice on whether the school's actions were justified and whether we still have grounds to take action against them.

THEIR ACTION IS NOT JUSTIFIED

Can My Wife Take Legal Action Against a School for Retaining Her Original Documents,

YES

Forcing Unethical Practices, and Pressuring Her to Resign?

YES

By the way :

what is her actual salary? 

What is her salary reported to Education Deptt/CBSE? 

What is her salary reported to EPFO?

(every school is highly vulnerable on this issue)