Can I install IMovie HD 6 if I already have IMovie 11 on my computer?

Happily this is easily achieved, but it has to be done backwards.

Delete iMovie 11 (just drag it to the trash). Now install iMovie 6 from the iLife 6 install disks. Update it to iMovie 6.0.3.

Now re-install iMovie 11. This automatically moves iMovie 6 into a folder it creates in your Applications folder called iMovie Previous Version.

Then reinstall iMovie 11.

iMovie 6 works great with iDVD 7.

Now you have them both, and you can have both in the Dock as well.

Another method is to copy the iMovie HD app from an older G4 or G5 Mac application folder and put it directly into the application folder on the Lion/Mountain Lion Mac, in a new folder you create there, calling it iMovie Previous Version.

You can easily create that folder (in your applications folder) yourself.

Yes, you will be able to use either version.

Neither. To make a playable version of the project you have to complete it, either by exporting it as Quicktime file (high quality) that you can then transfer to your laptop, OR by making a proper mpeg2 DVD file using iDVD to either make Disk Image of the file, or an actual DVD.

Do not move the iMovie project from one Mac to another, you will only mangle it!