Can the Department ask for more information than what assessee is submitting to it in the Form ST-1 and ST-3?

Yes. If it is felt necessary, the Department can call for additional information/ documents for scrutiny, as per Rule 6(6) of the STR, 1994 and Sec. 14 of the Central Excise Act, 1944 which is made applicable to Service Tax matters, as per Sec. 83 of the Finance Act, 1994.

Rule 5A of STR, 1994 provides that every assessee, on demand, is required to make available to the central excise/service tax officer authorized by the Commissioner or the audit party deputed by the Commissioner or the Comptroller and Auditor General of India, within a reasonable time not exceeding fifteen working days from the day when such demand is made, or within such further period as may be allowed by such officer or the audit party, the following records/documents for the scrutiny of the officer or audit party:
i. the records as mentioned in Rule 5(2) of STR, 1994;
ii. trial balance or its equivalent; and
iii. the income-tax audit report, if any, under section 44AB of the Income-tax Act, 1961 ( 43 of 1961).

However, such officer/audit party may allow further period for submission of the aforesaid records/documents.

In the event of failure to make available the records/documents, a penalty of Rs. 5000 or Rs. 200 for every day during which such failure continues starting with the first day after the due date, till the date of actual compliance, whichever is higher, is imposable on the assessee under amended section 77 (with effect from 12th May, 2008).