MacBook – Does a MacBook Pro need a power adapter to work in the Bahamas

The video out on MacBook Pro uses a Displayport / Thunderbolt port. To hook up to a VGA or DVI cable, you need an adapter. Alternatively you could buy a cable which has Displayport on one end and DVI or VGA on the other. The adapters don't come as standard so you'll need to buy one in an Apple store, online or use a third-party cable.

You can use it, but how much actual charging goes on may be minimal. It depends how much power your MBP is drawing (i.e. if you're doing CPU or graphics intensive tasks, you'll draw more power, thus less charging), but I suspect the 45W won't do much more than slow the rate of battery drain. If your MBP is asleep or turned off, it should charge the battery, just slower than the standard charger.