More context is needed before any absolute answer can be given. Without more context, I suggest that the following are the versions I would expect: 1-King Lear was written by Shakespeare. 2-He is/was/has been unaffected by his father's passing.
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navitasan1-King Lear is written by Shakespeare.King Lear is way too old to be "is". It was written by Shakespeare. (Shakespeare wrote it, not Shakespeare writes it.)
navitasan2-He is unaffected by his father's passing.Correct. ("unaffected" is an adjective, not part of the non-existent verb "to unaff