Add "Remove Connection" and other similar links to CB Content Module

How can I add links like the "Remove Connection" or "Report User" to the CB content module?

Substitute in the CB Menu tab it self and you can render its menu structure directly in the module. This is done with the below substitution.

[cb:usertab tab="17" user="#displayedOrMe" /]

The alternative is to a manually construct the URL for those actions.

How can you manually construct the url for "Remove Connection" for example?

You won't be able to use the popup form unless you also handle the cbTooltip usage it's using. I suppose you could just copy its HTML and replace the user id with a substitution. You can also use the direct link as follows if you don't care about the message popup.

Add Connection:
index.php?option=com_comprofiler&view=addconnection&connectionid=USER_ID

Remove Connection:
index.php?option=com_comprofiler&view=removeconnection&connectionid=USER_ID

Report User:
index.php?option=com_comprofiler&view=reportuser&uid=USER_ID

To get the displayed users user id you'd use the below substitution.

[cb:userdata field="user_id" user="#displayed" /]

How about displaying a message of an incoming connection request?

Your login module can show a link if the user has connection requests. Edit your login module and under Logout Options enable "Connection Request Notifications". Alternatively you could use a CB Query Field to query for the pending connection requests then use a substitution IF statement in a CB Content Module to condition a message to display if they've pending requests by conditioning the value of the query field.