My Startup disk partition is just 20 GB and I'm running out of space.
What's the safe way to transfer Applications folder to the other partition?
Can I just move all apps into a folder on the other partition and create a symlink to it?
Just move them is probably the best solution. The user caches and preference files stick with the user home folder, so other than convention - most cases it doesn't really matter which volume contains an application. You'll need
Spotlight still indexes them, updates to the App Store work as long as the drive stays mounted when you want to see that an update is available.
Tools like LaunchBar and others will probably need hand-holding to find your moved applications - especially if you don't place them in /Applications on the destination volume.
You will need to re-introduce the moved copies of the App to Launchbar, but in some brief testing, the following apps worked flawlessly when moved to the root of an external drive.