Articles and determiners

A test item I saw:-

__________ bird is flying in the sky. (The instruction is to fill the blank with a, an, the)

I feel that this is a poorly designed test item. As it is, I would fill the fill with 'a' not 'the' although it is not wrong to use 'the' in the sentence.

The other item I have item with is the following sentence in the same test:-

My teacher gave us _____ pages of homework yesterday. (The instruction is to fill the blank with 'many', 'some', and 'few'. I think the best answer is still 'many', but I am not to able to explain the use of 'many' over 'some'.