Is it possible to move ..\ampps\www directory outside of ..\ampps?
if not, Question 2:
Is it possible to setup a wildcard alias that would pull the site from an external directory (ie: Dropbox).
Yes. They are possible but you will have to do it everything manually by referring Apache Manual. You can move Ampps/www directory outside Ampps by changing DocumentRoot directive in httpd.conf
if not, Question 3:
Obviously, I can setup an alias for each site but with 60+ sites, three different computers, this could take awhile. Any advice to simplify syncing the files?
Sorry. Currently you can add only one alias at a time in AMPPS.
If all your 60 site names and directories have same pattern you can write a PHP script and create a conf file. Then just include that conf file in httpd.conf. You can get the alias pattern from "path/to/Ampps/apache/conf/extra/alias.conf". First add an alias from AMPPS to get the pattern.