According to the End User Liscense Agreement, Adobe allows you to install Photoshop on two computers so long as both aren't used at the same time or by different primary users. So, installing Photoshop on your second computer should not be a problem and not need any explanation or clearing up with Adobe.
If you upgrade to a computer that does not currently have Photoshop installed on it, the installation will ask you to insert the CD for a previous version to verify that you have a legitimate copy and therefore are eligible to pay the upgrade price instead of the full price. You do not need to install the previous version. If you do have version 6 installed on your second computer, it shouldn't be a problem (see above).
I believe from what I recall reading on the Abobe Photoshop User to User forums at
www.adobe.com, is that you can upgrade from almost any previous version of Photoshop. However, if it's version 5 or older, you'll need to call Adobe for installation instructions as the installer won't recognize it. But I believe it is possible to do.
--Racc