Sir,
Rule 6 (6) (vii) of Cenvat Credit Rules, 2004 stipulates that "the provisions of sub-rules (1), (2), (3) and (4) shall not be applicable in case the excisable goods removed without payment of duty are goods which are exempt from the duties of customs leviable under the First Schedule to the Customs Tariff Act, 1975 (51 of 1975) and the additional duty leviable under sub-section (1) of section 3 of the said Customs Tariff Act when imported into India and are supplied,-
(a) against International Competitive Bidding;
The above condition can be held satisfied provided excisable goods manufactured in India are similar to goods imported from abroad and are exempted from duties of customs leviable under the first schedule to the Customs Tariff Act and the same are supplied against International Competitive Bidding
Sub-rules (1), (2) and (3) of rule 6 of Cenvat Credit Rules provides various option to the assesse if credit availed inputs and capital goods and credit of service tax paid on input services are utilized in the manufacture of dutiable and exempted excisable goods or used for providing taxable and exempted output services. These provisions are not applicable if you satisfy rule 6 (6) (vii) of Cenvat Credit Rules, 2004.
Therefore answer to your first question is No. The answer to your second question is also No since goods supplied against International Competitive bidding are not exempted excisable goods.