How to Calculate the Notice Period

If I am employed under a 1 year contract since May 12 with a monthly salary of $2000, and I would like to tender a resignation on 3rd Feb, will it mean 3rd Feb is my last day?
Depends on the notice period required, by doing so, you are giving one day notice which you will be required to pay the company the salary in lieu of notice.

And also, what is the estimated amount salary-in-lieu that I will have to pay back to the co?
Depends on what is stated in your contract, if is one month notice, it will be $2000

Are there any other charges apart from the salary in-lieu? (i am being employed under a 3rd party agency)
Nope, unless otherwise stated in your contract.