Comprehensive and Detailed Explanation:
Option B is correct: A Variation is a formal change to the Works instructed by the Engineer via a Notice (Sub- Clause 3.5). This includes changes to design or execution such as slopes on a road.
Option A is a proposal, not yet a Variation. Positive interest does not constitute a Variation.
Option C is partially correct but depends on formal instruction after proposal acceptance; the question specifies the Engineer instructs the Variation, but since it was a request for proposal first, the Variation instruction comes later. Without explicit instruction, this is not yet a Variation.
Option D is invalid as verbal instruction plus a Notice denying cost claims does not constitute a proper Variation.
References:
FIDIC Yellow Book 2017 Edition, Sub-Clause 3.5 - Variation Procedure
FIDIC Contract Manager Study Guide, Module on Variations and Change Management

Option B is correct: The Contractor must obtain approval from the Engineer/Employer before making design changes.
Option C is correct: The Contractor can submit Value Engineering proposals to improve efficiency or reduce costs.
Option A is incorrect; unilateral changes are not allowed.
Option D is incorrect; Value Engineering can be proposed even after initial submission.
References:
FIDIC Yellow and Silver Books 1999 Edition, Sub-Clauses 4.1 and 4.4
FIDIC Contract Manager Study Guide, Module on Design and Value Engineering