As far as #1 is concered, use STSADM to backup the old site  and then do a direct
restore to the new site name. STSADM will create  the new site using the same
layout, permissions, etc. As far as #2 is concerned, you would need to create a
new site using the new template. From there, I believe you can use SMIGRATE to
move content, but I'm not too sure...

When you create  the new site  for question #1 you will also have to
create a new Content DB unless you delete the old site prior to
restoring the new one.

For #2 you do mean a new template  and not a new theme, correct?

you mention that I will loose all permissions. Is that all I'd
loose migrating a site  into a new template?

I don't know the full impact. Several things, like anything
chrome-related, user  permissions, groups, custom permission levels,
navigation, etc. would not migrate. I assume there could be more...

In WSSv2, you can use stsadm.exe -o backup -filename c:\file.bak -url
http://webapp/path/sitecollection to backup a site. If the site  will
exist in the same Web app, you must then delete the existing site before
restoring. Otherwise, you will get an 'instance not found' error on
restore. This error occurs because each site collection is assigned a
unique ID, and two guids cannot exist in a single content  database. If
you are not comfortable deleting the original site before testing the
new site (that would be me!) then I would create  a second content
database for the Virtual Server and restore  with the new name. Once you
are comfortable that the new site works correctly, then remove the old
site. Be aware that hard-coded links will not change on the rename
(backup/restore).

To restore, stsadm.exe -o restore -filename c:\file.bak -url
http://webapp/path/newSiteCollectionname

1. I would NOT use smigrate in WSS v2 because it does not preserve
permissions ( it does in WSS v3)

2. Sorry, a template  is like spray snow... once you spray it,
changing the template won't change the snowman! You could always use CSS
(themes) to achieve some customization. In WSSv2, you will lose all
permissions. If this was WSSv3, you COULD do a stsadm.exe -export |
stsadm.exe -import to achieve some of what you desire. It will import
into a new SC, with a new theme.