Bangalore private teacher laws

There is no necessity for your wife to sign a fresh bond altering the conditions of the employment.

Besides the school uthorities cannot hold back her certificates, it is illegal 

Your wife can refuse to accept the lower post with lesser salary and can refuse to sign or accept their dictates, let them take action, she can challenge them legally

Also, they have a stupid rule where if a teacher takes 1 day extra leave on top of the allocated 10 days of Dussehra leave, they deduct the salary for the whole 11 days.
My wife had told the principal in advance that she had to visit her father who has stage4 cancer and will need 2 extra days of leave. The prinicipal had verbally agreed to this and had asked to submit a written request, which my wife did. But I'm feeling she will not honour that agreement due to this incident.
Can we take any legal action in case they deduct the 11 days salary?

If the employment terms and conditions were read and understood before accepting or signing the agreement then it will be of no use to take any legal steps to express your frustration or dissatisfaction . 

if you violate the conditions of the employment then the management may reserve its rights to initiate legal action as per their rules, however that will not empower them to deprive your basic rights or the constitutionally protected rights in this aspect. You may consult a local advocate, discuss the issue at length and take appropriate action which is warranted to this situation, provided the issue is beyond your control

The norms followed by said school are just conditions laid down by them, and they have no right or authority to impose any condition which violates the ordianry rights of the citizens. Imposing the arbirary bond, forcing the employee to take up another post against the will of the employee that too, at a lower salary, excessive deduction of salary, witholding the original certificates etc. cannot withstand the scrutiny of law. 

However, it is not that easy to seek justice through a civil action. Remedy, in my view, lies in approaching quasi-judicial forums such as Human Rights Commission, Womens Commission, Legal Services Authority etc.

Prima facie it is an unaided private and not a government or government aided school, where such practices are followed, isn't it ?

Primarily you have sought advise only from those experts who know Kannada Laws.  Probably you  did not know that there can be central law also to your rescue.

However,

Employer is at liberty to change the job. Even govt officials as high as IAS/IPS cannot avoid this.

But reduction of wages is not permissible.

She already appears to have been underpaid.  In all probability her Provident Fund is also under deposited

These schools (if recognized by state Govt) are bound to pay the salary as per govt scales which in any case is going to be much (much) beyond Rs 17000/-.  They are bound to submit report of wages to the distt education officer [and also to CBSE/State Education Board, if teaching metric and above].

These details are available in RTI.

As per another central Law (not Kannada Law) they are bound to deposit the Provident Fund in the office of RPFC Bangalore, as per the pay scale they are official giving.

This situations going to be much uncomfortable for the management. EPFO will recover actual PF of all employees from the day they employed 20 employees (including daily wage/ ad-hoc etc)

As far as deposit of originals is concerned you may meet a local lawyer for examining feasibility of complaint under Bonded Labor Act.