Solution:
'is' is used with singular subject. 'You' is a singular subject. Hence, 'is' is the correct answer.

Solution:
The sentence is in past tense and therefore 'was' is the correct option to use. No other option is suitable.

Solution:
Did she run away yesterday?

Solution:
Neither allows us to make a negative statement about two people or things at the same time. Neither goes before singular countable nouns. We use it to say 'not either' in relation to two things.

Solution:
Wings of Fire is an autobiography of APJ Abdul Kalam.

Solution:
'at the moment' clearly indicates the sentence is in present continuous and therefore 'is writing' will be the correct answer.

Solution:
'caused by' means make (something, especially something bad) happen. As the sentence is in simple past tense 'had' or 'had been' is not used.