For the first question, edit the page to set it up as you want (removing/adding webparts as required), then save the site as a template...making sure to check the box to include content if there's anything you want to show up on the site by default.
For the second, this will require a little bit more work to accomplish, but is still a relatively simple operation.
Connect to your site through SharePoint Designer. Once there, open the default.aspx page for the site (should be at the bottom of the list) and select the "right" zone through the designer. When selecting this, you'll see the html highlighted in the upper window. Hit the "delete" key to remove the html for the zone. Once you've done this, you'll need to remove a few extra table cell tags to make it so the left column will stretch over to take the rest of the page. Immediately above the part of the html you removed, delete the remaining tags between the first "</td>" (immediately after the closing "</WebPartPages:WebPartZone>") and the closing "</table> tag.
It will look like this before:
</ZoneTemplate></WebPartPages:WebPartZone>
</td>
<td> </td>
<td valign="top" width="30%">
</td>
<td> </td>
</tr>
</table>
It should look like this after:
</ZoneTemplate></WebPartPages:WebPartZone>
</td>
</tr>
</table>
After you make these changes, save the page. Go back to the site and refresh the default page of your site and you'll see the changes applied. Now, go back and save the site as a template (as mentioned in the first answer - also making sure to check the "include content" box if you need to have any default content show up on the site) so you can use this new layout to build additional subsites.
For the third question, I'm sure there may be an easier approach, but here's what I normally do. Open the site in SP Designer, select the table that contains the zones and modify the html to rework the layout (ie: instead of a 2 column table where the zones are layed out side-by-side, make it a 1 column table with them layed out vertically). If you're familiar with formatting tables through html, this shouldn't be a problem. Additionally, if you just want to modify a specific *zone itself, you can "right-click" the zone in the designer and look at its properties (or in the html "right-click" and choose "tag properties") and change it to either vertical or horizontal layout (*this has no impact on how the 2 zones stack, just for the webparts in the individual zones themselves).
Hope this helps,
- Dink