[[ If I want to get the applications from my old hard drive to put on my new Macbook Pro, is it as easy as copying the application over and the folder in Library that contains all the data? ]]
Sometimes that works.
Sometimes it doesn't.
It depends on WHICH applications you're trying to "copy over".
This is because if you do only a "finder-manual-drag 'n' drop" style copy-over, you may not be copying essential files/folders in other locations that are required for the app to run.
Another way that might work better is to use Migration Assistant, and choose to only migrate your "Applications" folder. MA will also transfer any support files. BE AWARE that even when you do it this way, you may be required to re-register some apps.
The unwanted "benefit" of using MA to move things is it moves ALL your apps -- you can't "pick and choose" among them. I'd like to see MA updated by Apple to permit the user to select individually the apps to be migrated, vs. those to be left behind.
Another way to do it is to "re-install fresh" from your original discs or dmg files.