How soon do Universities process applications? How long does it take for a student to receive an offer from a University applied for?

An offer letter from a University where a student meets the entry requirement and eligibility criteria is generally issued by the admissions team within 48-96 hours of the admission team receiving the application. Applications are generally forwarded by agents or by a student enrolment advisor or a similar team in the University. Universities accepting students directly accept applications from students directly too. It should take a maximum of 96 hours from the time the application is logged in to receipt of a conditional offer letter. 

Does it help me if I submit my application for the same university to two or more agents? I can then pick up the best discounts by forcing their hand? 

Submitting an application with more than 1 agent for the same University actually delays the arrival of the offer letter. That is because admission teams have a Change of Agent, or COA process whereby duplicate applications received either together or one after another, are checked with the agents and the agent handling teams to which agent the application should be awarded. If one agent has submitted your application, and then another one does it too, then you should expect a delay of upto 7 days before your application to be processed. This is the time taken to resolve agent conflicts. And if you keep on hopping from agent to agent, rest assured it will indeed take a long time to resolve all agent conflicts.