You could have given complete details in your first post itself.
You were on unapproved leave.
However you have submitted leave application and specific reason for seeking leave and your leave application has been acknowledged.
What is your designation? Are you selected as a trainee under standing orders, or as apprentice under Apprenticeship Act?
You have posted that” also though we were on probation we were put to work directly after just 2 weeks of trainin while joining.”
This may go in your favor.
Do you have record to establish it?
You may go thru the enclosed judgment.
How many employees like you were recruited as trainee and then put to work directly? What is the total headcount in company and what is the percentage of such trainees in the head count?
All employees may join hands.
You have posted that;
----“1. Due to personal problems I wanted leave so I intimated via letter immediately to the higher officials and requested for one month leave without pay explaining my situation.
2. They did not reply until ten days passed by and then I received a letter blindly stating I was am on unauthorised absence without any intimation whatsoever.”
Here you cited some letters and replies in writing.
Later you have stated that “They Told” implying these transactions are verbal, and not on record. You should have placed these representations and replies on record in writing, under acknowledgment.
----“ 5. Then they replied stating the authorities have decided to accept my resignation despite me being on unauthorised absence subject to me paying the bond money befor the specified date-10th.”
This may become an imp. document, on record for you.
You may approach a competent and exeprienced labor consultant/service lawyer, well versed with such matters, show all documents including job advertisement, offer letter, joining report, appointment letter, standing orders/training scheme of the company and policy{ these may be on intranet, employee portal, HR page}, bond, your communications to company and replies, and give inputs in person, and let your lawyer evaluate the merits, and suggest appropriate forum if the need be.
Let your lawyer structure your further communications to the company to suit you in the long run.
The company may yield to legal notice of your lawyer or you may have to agitate in appropriate forum.