You can install new apps to your ~/Applications folder (the folder is already there), but they are only accessible to you. No other negative to doing this.
Don't move any app that came as part of the operating system, or any iLife app. If you do, you will not get automatic upgrades correctly through software update. I thought I would make sub-folders in my Apps directory when I first got an iBook, and learned the hard way.

You *might* be able to fix this by removing and re-installing the programs to custom locations. But just save yourself the heartache.
If you're really OCD about organization, though, it makes a lot more sense for the apps to not be in your home directory. Your home directory's permissions are all wrong, and you create this weird system where you have a folder that's supposed to belong to root:admin under your folder. What you want seems a lot less organized and clean to me than the way Unix OSes work in general. But if it makes you happy, have at.