Mac migration does not work with Cloud programs... are you on a Mac?
Yes, you need to download and install again... but there is no added Adobe fee
Cloud License allows 2 activations http://www.adobe.com/legal/licenses-terms.html
-Install on a 2nd computer http://forums.adobe.com/thread/1452292?tstart=0
-Windows or Mac does not matter... 2 on the same operating system, or 1 on each