If a hotel enters into a contract with a Vendor for supply of man power for Cleaning services and almost 30 different persons are provided by the vendor for work in different shifts in any month.Does it attracts ESI ? If it attracts then What are the obligation on the hotel who is paying that contractor?

The hotel has to have a license to engage the employees through the agency. Check up whether the Agency has ESI code and has covered the employees working in your orgnisation/hotel. To be sure get into a contract with the agency that it will absolve the hotel of any liabilty towards various labour legislations.

Is there a law that restricts lady staffs from doing night shift.

Yes,

The local state administration is putting restriction on lady staffs from doing night shift. see the link :

http://labour.kar.nic.in/labour/karshopscommercial-1961.htm

Relevant extract from the above link:

The employment of children below 14 years is prohibited under Section 24 of the Act.  Young persons and woman shall not be employed during night, between 8 pm to 6 am.

Yes. The prohibition of children employment is again subject to the work place. Ex: Domestic help