I agree with answers 1-14, and 17-20. I don't disagree with 15-16; I just don't know the answers.
On #5, you are short the call, so it wouldn't make any sense for your option value to increase when the position moves against you.
On #7, you are short the 0.50 delta put and the underlying price goes down. Firstly, its a put so it is actually -0.50 delta. Secondly, a drop in price of the underlying causes a decrease in delta (of both puts and calls), so -0.50 - 0.03 = -0.53.
On #11, just remember that delta is supposed to represent the % chance of the trade finishing in the money. So as time passes, the % chance that an ITM option will finish ITM increases and conversely the % chance an OTM option finishes ITM decreases.
On #13, if you're short stock, selling calls doesn't hedge the position. A drop in (stock) price would help both trades and an increase in price would hurt both trades.