I have master site and subagent.master subdomain, the same database different prefix. I use k2 and everything works. Changes to the modules are not visible on subagent.master subdomain?

I don't know if I have understood clearly your question.
There is 2 things.
If you want to share the content of K2 between the website, this is possible when you create the slave site. In this case, you have to create a specific JMS Template rule where you specify that the K2 content is shared.
This decision must be taken when you create the slave site and can not be taken after that the website is created.
The reason is that the "item id" with the content must be the same in the different website. This is only possible when creating the slave site, because at that moment, the K2 table of the slave are replaced by a link to the original table.

Concerning the properties or attributes that you may use in a menu or module that display a content, they are independent as this settings is generally stored in the #__extensions table of the core of joomla that can not be shared.
So this is normal that a settings of a module is not shared between the sites.

OK, I know for K2. I just listed it as something that works OK.

If I have a custom module that contains text, when I edit this text on the master site, it will not automatically be corrected on slave site.


I understood correctly?

Yes but for the Custom HTML, you can buy the Multisite Custom HTML module that allows you sharing the content AND also decide if you want to have the physical Custom HTML parameters that are applicable on the Multisite Custom HTML.
See www.jms2win.com/en/joomla-multisite?page...64&category_id=1