Utility maximization in a 2-good scenario with an option to buy a combo of the two
Your answer to Q1 is correct. 

For Q2, a little graphical intuition would help. 

Suppose you spend all your income on the combo, you'd be able to purchase $80$ movies and $20$ books. This is the point $(20,80)$ on the $(x,y)$-plane. 

If you buy $1$ less combo, you'll have $76$ movies, $19$ books, and $\$50$ cash. Spending the entire $\$50$ on movies would move you to $(19,81)$; spending all the cash on books would move you to $(21,76)$. (Of course you can split the cash between the two goods, but it's easy see on a graph that such a split is not efficient.)

Therefore, trading one combo for movies implies a relative price of 1 book for 1 movie, and trading one combo for books implies a relative price of 4 movies for 1 book. Using the information, we can plot the budget constraint as below: 

The green segment, given by $y=100-x$ ($x\in[0,20]$), represents trade-off between the two goods implied by switching from combos to movies. The red segment, given by $y=160-4x$ ($x\in[20,40]$), represents the trade-off implied by switching from combos to books. It is clear from the graph that no other ways of using the income is more efficient. (As a reference, the budget line without the combo is plotted using the black dashed line.)

Given this budget constraint, it should be straightforward to solve for the optimal consumption bundle.