Can i install all my applications on an external hard disk and leave the main hard disk alone?
You can! And there are a few distinct advantages of such an approach too, because OS X handles applications differently from Windows, the main advantage being a sudden logic board or hard disk failure will not take down your work since you have everything stored on an external media: just connect your external hrad disk to another Mac and you should be up and working in no time. (assuming that you hvae more than 1 Mac at home, that is.) Remember that OS X applications are all self-contained in an .app folder. This is different from Windows, which rellies on DLLs and registry keys.
Installing an application on an external drive is the same as installing it as one would on the Mac’s main hard disk: just drap and drop the .app into the external drive. And you can run it from there once the application has fully copied itself over.
If the application comes with an installer package, just run the installer like you would for a normal OS X application installer, clicking ‘yes’ until you reach the part where you are prompted to select an install location. Select your external drive and proceed with the rest of the installer as usual. Do take note, however, that some applications will not permit you to install them on external media (especially drivers).
Once you have completed the installation/drag-and-drop, just run the application from your external hard disk. There is likely to be a performance penalty, since USB/Firewire is usually slower in data transfer as compared to SATA.
However, do take note that any application that is installed via an installer on your external hard disk has some problems if you are using the external hard disk on another Mac. Firstly, the initial startup of the application will be significantly slower because the application needs to create support files in the Mac computer it is connected to in order to ensure that it can run. These support files are not very large, but they do have a significant impact on the initial start-up time of the application. (This is especially true if you are running an application like NeoOffice on an external drive)
In addition, applications that require a serial number or an activation code (eg: Final Cut Express, Adobe CS, MS Office, etc) to run will not work if the hard disk is connected to another Mac; the application will insist on an activation or serial number before you are allowed to continue using it, as files containing information about its activation are stored on the Mac it was installed on, which are naturally absent in another Mac.
That said, having your work stored on a portable medium is still a very good way to ensure productivity if your current Mac suddenly dies from hardware failure. Just remember to make backups of your external hard disk, otherwise you’d be finished if your external media dies on you.
Last but not least, remember that even if your hard disk is formatted as FAT, the applications you’ve installed will not run if you plan to connect the hard disk to a Windows PC (your documents should still work). And naturally, a HFS formatted hard disk cannot be read by Windows at all.