This is a very hard question. In EA 1955, employers are required to make "Due Inquiry" before giving out punishment due to misconduct. You can argue that a straightforward misconduct such as lateness does not require inquiry since you can just refer to the attendance record. Therefore, you've already cleared the "Due Inquiry" requirement.

The contract has no effect in terms of Section 20 IRA 1967. The employee can also claim that he or she had to sign the letter under duress / pressure from the employer.

If the employee is not subjected to EA 1955, as long as the employee consent it, it should not be a problem. But beware of the 60 days claim period under IRA 1967. The employee can make claim of unjust dismissal regardless of the contract that he / she has signed consenting T&C variance.

Okay. Unless the employer issues a letter and employees agree with that.

If the employer insists to do so without the employees' consent, it would be ground for claim of Constructive Dismissal.

I don't think unilateral variance of contract is allowed. Unless there is a clause in the Employment Contract that allows so.