In both cases, you should argue along the lines of options arbitrage. If you think an asset (or a portfolio) is relatively cheap (as in: arbitrageable) then you simply buy low, sell high.
In your first case, it seems that the call is too cheap, as in:
So let's buy the call, sell a put, short a unit of stock, and borrow some money:
Your understanding is correct. It makes no sense to exercise a call (as well as a put) when there is time premium remaining because you are throwing away that time premium by doing so. Sell the call and buy the stock if you want to own it in order to capture the dividend.
Buying the stock to capture the dividend makes no sense to me if it's a non sheltered ...