To check a user is login to WordPress is_user_logged_in() function can be used. is_user_logged_in() This function may also be used to add Login/Logout Button.
At WordPress admin Dashboard there are a number of widgets for showing activity, quick drafts, news etc. These widgets installed by default. These widgets can be removed by using remove_meta_box() function. Either you can remove widgets of your choice or remove all widgets. For example remove ‘Activity’ widget then below line work for you. remove_meta_box( […]