[TYPO3-english] Typo 6.2: extbase extension and fluid

[Ph Typo]

Hello
I am beginner with typo3 and have a following issue:

I created an extbase extension with some domain objects. There are also some relationships and some actions per each domain.
Then I created an empty page in typo's backend and added my plugin to this page.
What I would like to achieve is to have a possibility to have a page for each domain object, where I could do some user's defined queries and CRUD operations.

My approach was to create pages in typo's backend, where I could define (with Typoscript) which action and controller I would like to use, f.e.:
page=PAGE
page.10 < styles.content.get

page.10 = FLUIDTEMPLATE
page.10.format = html
page.10.template = FILE
page.10.template.file = typo3conf/ext/register/Resources/Private/Templates/Register/List.html
page.10.layoutRootPath = typo3conf/ext/register/Resources/Private/Layouts/
page.10.partialRootPath = typo3conf/ext/register/Resources/Private/Partials/

page.10.extbase.pluginName = Register
page.10.extbase.vendorName = NewVendor
page.10.extbase.controllerName = RegisterController
page.10.extbase.controllerExtensionName = register
page.10.extbase.controllerActionName = list

In this situation I get List page but without data from the database - all variables defined in my controller are displayed as NULL in my template.

However, when I leave only this fragment:

page=PAGE
page.10 < styles.content.get

data from the database is loaded into the page but as you can see I cannot choose template from the plugin. The default template is loaded based on configuration in ext_localconf.php (and it is List from Register).


I also tried another approach: I used action-links in my fluid template, f.e. 
<f:link.action action="list" controller="RegisterController">list Register</f:link.action>
but without success. 

Don't know if these approaches are reasonable. Do you have any hints?

I have to use typo 6.2

Kind regards
Paul