1) As per Section 16 of Civil Procedure Code, suits pertaining to property shall be instituted in the court within the local limits of whose jurisdiction the property is situated. Since the property is located at Indore (Madhya Pradesh), the courts at Indore alone will have jurisdiction over the rental agreement.
2) The Stamp paper can be purchased in any of the state of your choice. However if you choose to register the rental agreement in a sub registrar office, registration and stamp duty shall be as per Rules prevalent in Madhya Pradesh. Also since you are planning for 11 months agreement, it is not mandatory to register the rental agreement.
3) A 11 Month rental agreement should not have any extension clauses or escalation clauses. If any of the wording in the rental agreement indicates a tenure beyond 11 months, then you need compulsorily register the rental agreement by paying registration charges and stamp duty at Madhya Pradesh , failing which the rental agreement will be void in eyes of law.
4) The best option would be to enter to a fresh rental agreement at the end of 11 months or opt for fixed tenure rental agreement with rental escalation clauses and register the rental agreement by paying stamp duty and registration charges.
Hope this information is useful.