In this question:
What problems will this cause for individuals and society?
Which parts of speech are cause in this question? If it is a noun, why isn't there be before this cause? If it is an adjective, what is the role of this ?
'Cause' in the sentence given is neither noun nor adjective, it's verb.
To understand this try answering your question - This will cause the problems like .... to the individuals and to the society.
cause (noun) - the reason behind some action.
Examle: The cause of our country's plight is corruption.
Or as you asked use of be look at this:
Corruption is the cause of our country's plight.
to cause (verb) - to make something happen. Lack of exercise causes ill health.