If I remove GarageBand and iMovie from my MacBook Air, can I restore them later?
You should be able to download them with your Apple ID (the one used when you bought or registered your new Mac) from the Mac App Store.
You can try to log in, and then see if you have access to them (you should also have access to the OS X, so you can re-install it too), otherwise you should contact Apple, so you get access to the free apps - and OS X Mountain Lion.
http://support.apple.com/kb/HT4718

Restoring iLife applications after Internet Restore of OS X Lion or OS X Mountain Lion
If you erase install OS X Lion or OS X Mountain Lion on a new Mac that shipped with OS X Lion or OS X Mountain Lion installed, you can download iPhoto, iMovie, and GarageBand from the Mac App Store.

After installation, start (up) from OS X.
Double-click the App Store icon in the dock.
Enter your Apple ID and password.
Click Purchases.
If you haven't previously accepted your bundled iLife applications within the Mac App Store, you should see your iLife applications appear in the Accept portion of the screen. Click Accept.
You may be asked for your Apple ID and password once again. Your iLife applications now move to the Purchased section. These applications are part of the software that came with your Lion based computer. Your account will not be charged for them. Click Install to complete installation of your applications.