Option A is correct. Under Sub-Clause 11.9 (Performance Certificate) refusal or incorrect issuance by the Engineer, combined with disagreement by the Contractor, may cause a Dispute to arise.
Option B is correct. If a Party is dissatisfied with a determination, it must give a Notice of Dissatisfaction (NOD) within 28 days to escalate the matter to a Dispute, allowing either Party to refer it to the DAAB as per Sub-Clause 21.4.
Option C is incorrect. The contract does not specify a 42-day time limit for submission to DAAB after NOD; timelines vary by contract and stage.
Option D is incorrect. 'Disagreement' is not a formally defined term in FIDIC contracts, whereas 'Dispute' is.
References:
FIDIC Red, Yellow, Silver Books 2017 Edition, Sub-Clause 11.9 and Clause 21 - Claims, Disputes, and Adjudication FIDIC Contract Manager Study Guide, Module on Dispute Resolution

The Contractor's obligation to submit progress reports continues until all outstanding work identified in the Taking-Over Certificate has been completed. The Taking-Over Certificate signals substantial completion but may allow for outstanding minor works. Reporting is essential to monitor progress on these outstanding works.
The Performance Certificate relates to final contract completion but reporting usually ends earlier only after all works are completed.
Therefore, Option D is correct.
References:
FIDIC Red Book 1999 & 2017 Editions, Sub-Clause 4.21 - Progress Reports FIDIC Contract Manager Study Guide, Module on Communication and Reporting

Comprehensive and Detailed Explanation:
The Contractor may submit Value Engineering proposals to improve efficiency or reduce costs; however, it is not an absolute contractual obligation to submit such proposals. Also, the preparation of these proposals is generally at the Contractor's own cost initially. If the proposal is accepted and results in a Variation, then adjustments to the Contract Price may occur, potentially reimbursing the Contractor.
Thus, both statements are false.
References:
FIDIC Red, Yellow, Silver Books 1999 & 2017 Editions, Sub-Clause 13.1 - Value Engineering FIDIC Contract Manager Study Guide, Module on Variations and Value Engineering

Under the FIDIC Red Book 1999 Edition, the Engineer is generally responsible for issuing determinations on claims and contract matters. However, if the Particular Conditions require the Engineer to obtain the Employer's prior approval before issuing such determinations, the Engineer's options become limited if that approval is not granted.
* Option C (Issuing the determination to the Contractor in the form and with the content agreeable to the Employer, with a remark that it is the Employer's determination and not the Engineer's determination)is a practical approach often taken. The Engineer may issue the determination as directed or approved by the Employer but must clarify that it reflects the Employer's decision rather than the Engineer's independent determination.
* Option D (Informing the Contractor of their inability to issue the determination, due to lack of Employer's approval)aligns with transparency and procedural correctness. The Engineer should notify the Contractor if they cannot proceed with the determination, explaining the reason to avoid misunderstanding or delay.
* Option A (Remain silent and do nothing)isnot appropriate, as it may cause project delays and disputes.
* Option B (Referring the matter directly to the Dispute Adjudication Board)without a determination from the Engineer is not standard procedure under the 1999 edition. The Engineer's determination or failure to determine generally triggers the dispute resolution process, but referral is normally after due process, including issuing or attempting to issue a determination.
Hence,Options C and Dare the appropriate courses of action.
References:
FIDIC Red Book 1999 Edition, Sub-Clause 3.5 - Determinations
FIDIC Red Book 1999 Edition, Particular Conditions (typical clauses on Engineer's authority) FIDIC Contract Manager Study Guide, Module on Claims and Dispute Resolution

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