I will mention both conference and tourism in the application.
That part is extremely important. While mentioning the conference might led the Hungarian consulate to decline to entertain the application (see below), it would be even worse not to mention it as you would risk a refusal and black mark in your record.
Problem 1: I will get the NOC from the institute only for the conference. However, I can get the leave application from the department for Hungary/Switzerland tourism. Is that enough?
This, together with the mere fact that you would be attending a conference strongly suggest that the conference is the real purpose of the trip and therefore that Belgium is the main destination. Published advice from the EU Commission and implementation of this rule has been somewhat inconsistent but engineering a longer stay in Hungary should not be enough to overcome that presumption. There is a significant risk that Hungary therefore decline to process the visa on that basis.
Problem 2: Is the above plan enough to get the Schengen visa? Any suggestions about making the tourism itinerary to convince visa officer well enough. Is there any schengen country where I will get the visa with ease or less paperwork with the above conditions?
The rules are designed to make this impossible. You are not supposed to have a choice in where you apply and the rules are supposed to be the same across Schengen countries. In practice, there are some differences in their implementation but I don't think it would help in this case. From this perspective, there isn't and shouldn't be any solution to your problem besides waiting for an appointment with the Belgian consulate.
Problem 3: What is minimum balance to maintain in bank account, If I am applying for tourism of 2 weeks in Schengen coutry.
You can look at earlier questions and the link posted by @Traveller for guidelines. Do note that you might need more than a specific amount of cash in your bank account, it's also important to show that you can afford this trip based on your income.