@ Ashutosh
First of all i would like to answer all of the 3 questions you have asked respectively:
1) Is there any threshold limit for individual tax payer ( Salaried Person) in case of Rent Payment ?
Ans : Already Answered above by Mihir i.e. Rs. 180000/-. All assessee are liable to deduct tax except individual and huf covered u/s 44AB (Audit). Therefore, Individual Tax Payer (Salaried Person) is not liable to deduct tax even if u are paying a rent of Rs. 240000/- p.a.
2) Is the above person liable at any time for its Landlord's tax liability in case of Rent payment?
Ans: Individual Salaried Person will never be liable for Landlord's tax liability at any time in case of Rent Payment.
3) Is the employer of that salaried person is liable at any time on this Rent Transaction or responsible to ask the Pancard details of its emplyee's Landlord ?
Ans: Employer of that salaried person is not liable to any time on this rent transaction. However if the rent payment is large or u can say that paying more than Rs. 180000/- p.a. than he may ask the employer to furnish the details of pan of Landlord in order to ensure himself that the employee is actually paying the rent. In case the landlord refused to submit so details than employee may furnish the declaration to his employer regarding the situation and the most important, the employee must pay the rent via Cheque or Bank Transfer so that employee can proof the rent payment to anybody i.e. employer, etc as the landlord is not submitting any details. It will serve as a proof of rent.
So if landlord is not willing to give PAN Details, no body is liable in case of Individual Salaried Person. I suggest must pay rent via Cheque in order to serve proof in case of any dispute correspondings in future.