I would like to include a "Module K2 content" in my frontpage. But I would like to customize it by applying it a sub-template.

I´ve applied before a template to item.php on a specific category successfully by adding a sub-folder in /componentes/com_k2/templates (different from default) and editing the item.php on that folder.

When I´m editing the module "Module K2 content" there is an option to apply a sub-template. As I have seen, if I create a sub-folder in /templates/*current-template*/html/mod_k2_content/ it appears in the sub-template option, but I don´t know what is the php file that I need to edit in order to customize the "Module K2 content".

Sorry! I´ve already find the answer. It´s default php.
I have added a sub-folder not on /templates/*current_template*/html/mod_k2_content but directly on /modules/com_k2_content/tmpl and it works. And the copy the default.php and customize it.

Just to know if I´m right... the difference between put under the /templates/*current_template*/ or directly on /modules it´s that it would be applied just when a template is selected (in the /templates...) or always available (on /modules...)

And another question. how can I add a custom css for this modules?

You can create a css file override in a very similar manner to what just did.

Here are some joomla docs that show you the procedure.
docs.joomla.org/How_to_override_the_outp...rom_the_Joomla!_core
docs.joomla.org/Understanding_Output_Overrides

Also there is a shortcut method using a plugin that might make things easier.
extensions.joomla.org/extensions/style-a...ign/templating/14053

Let us know if you have more questions.

Cheers,
Ed