Choose the sentence in which the Modal has been used incorrectly:

The correct answer is Option (2) → Shall you show me the way to the station.

Will and shall in questions:

• Will you ...? is used to make a polite request to the listener.
• Shall in questions goes with I and we (Shall I open the window? Shall we go?), to offer or suggest.
• This sentence: a request to the listener needs "Will you show me the way to the station?"; "Shall you" is wrong here, and the question also lacks a question mark.
  Example: Will you help me carry this box?

Tomorrow will be Sunday. — Correct use: will states a simple future fact.

Need I write to him? — Correct use: need works as a modal in questions and negatives, followed by the base form "write".

Will you have tea? — Correct use: will you makes a polite offer.

Contrast: Will you ...? makes a request to the listener; shall in questions goes with I and we ("Shall I open the window?"), not with "you".