Please ensure you've latest release of CB Connect installed. Once done you need to create a new field of type "Facebook Social Plugin". Then from the drop-down select "Invite" under the "SITE" scope. This will give you a field that'll allow your users to invite their Facebook friends. Please note they have depreciated the API that the Invite feature uses and may or may not work exactly as expected.

Social Plugins are just text files where are parsed and rendered as jQuery. You can find and edit them within the below directory.

components/com_comprofiler/plugin/user/plug_cbconnect/facebook/social_plugins/

Please keep in mind the invite plugin was a painful process to create. It is using depreciated API, which Facebook has yet to replace and you'll have little control in its configuration.

then I can't translate the text that you can see in the attach image, and resize the width of the fb window?

As far as I am aware none of which you can do without massive work to the plugin. You can try loading a different localization of Facebooks JS API, but that may or may not work. As I've stated this is depreciated API (they no longer support, maintain, fix, etc.. it) and until they've replaced it with a valid social plugin it's in a state of "as good as it gets". Believe me I wasn't pleased with the results, but it was working which makes a lot of difference when users want FB invites.. to achieve working required 3-4 full days.

You can edit the invite.txt and change some of the strings, but not all of them as not all of them are defined by the social plugin it self. Some are just sent back from Facebook, which would require localization of their JS API.

The below strings can be changed.

"content" attribute: (contents of the msg the user will receive at Facebook)
You have been invited to join [site_url]!

"label" attribute: (what the button will say to click to go to your site at Facebook in the msg user will receive)
Website

"aciontext" attribute: (header in invite display)
Invite your friends from Facebook.

Not logged in message:
Please sign in with Facebook to invite.

Aside from the above there's no easy way to translate the rest.