To make sure that the user is active, you want to go to Customize>Users, and click on the Edit link for a user. In Step 1 of 10: General Properties, you need to make sure that you have a check in the checkbox for Login is Active.
In addition to that, in Step 4 of 10: Access to Tab Groups, you need to make sure that this user is assigned to the Tab Group of CRM.
In Step 5 of 10: Access to Roles you need to make sure that the users roles is the same as the role that is assigned to the tab of Activities and the tab link of Activity Calendar.
To verify those tab assignments, you need to go to Customize>Tabs and either select the Activities tab or when you click on the Edit Tab Links link for that activities tab, the tab link of Activity Calendar and that they are both assigned to this user.
If you go to Customize>Tab Groups and you select the tab group CRM, you also need to make sure that one of the tabs for this group is Activities.
In regards to the hide button, can you be more specific?
I hope that this helps.