I don't think so; specifically, in an era where government is looking at Higher Education Institutions paying their staff through internally generated funds (IGF). The corporate world can provide assistance in that regard.
I think in some issues such as diagnosis and lab control it isn't logical to donate all responsibilities to corporate but in some cases such vaccine application teams can be made of corporate.
In all situations government must keep it's supervisory action. I am totally agree with Dibakar Pal
As long as education and research is supported, that is good. However, if it is directed - see research on drug research and alternative methods, if researchers' livelihood is provided by corporate funding, it hinders the development.
I don't think so; specifically, the sectors enjoy the almost-market, the competitive integration of public and private with the State to act as regulator.
There are no universal answers to questions like this. Each society and state must answer the question to fit its local conditions.
In most 'western' societies there is a mix of state, corporate and charitable trust organisations funding medical research. Junior levels of education are state (taxation) funded while higher education is predominantly privately (personally) funded. Low revenue infrastructure issues like transport networks, defence, policing tend to be state funded while high revenue infrastructure such as fuel, power sources, air travel are largely corporate funded.
Similarly it would be wrong to equate corporations with limitations on education. Many corporations run and support extensive educational and research activities. However this is always tempered with a level of self interest by those corporations. So given modern conditions it is unlikely that corporate actors would ever fund something like LHC as the revenue streams are too small. However a very large proportion of medical research is corporation funded as there is money to be made by fixing the worlds medical problems.
It is also wrong to assume that universities aren't corporations and act in a purely ethical manner, funding only the best research. There is an industry called higher education which turns out degrees as a product.