And the template do not work.

When you check the links in top bar of the browser, you will see that they might be wrong when SEF is enabled.
The reason is that Joomla (not JMS Multisites) convert the links present in the menu and NOT in the "<form" content.
When you patch the joomla SEF sytem plugin to also process the <form action the links are better but another side effect is present due to the fact that when you submit a form with a post, Joomla does NOT read the post parameters for the option and items ID.
If you move the option and itemid in the <form action the joomla can find the "get" parameters.
This still have another side effect with some SEF settings because you can submit a form that is considered as a child of the URL containing the "menu" alias suffix. In this case Joomla is not able to decode the URL that might have parameters that it does not understand and therefore display the default option or the default menu.

We are currently testing a 1.2.37 that should improve the processing.
We have implemented a SEF routing to overwrite the default Joomla SEF processing in aim to avoid the joomla SEF encoding/decoding inconsistencies.
The current implementation seems to be compatible with Joomla 1.5 & 1.6 core SEF but not with all SEF extensions. AceSEF 1.5.1 is OK but not sh404SEF.