To see user profile, click on the profile or click on the menu icon on the right of the bar and choose Contact info.
The Last seen is shown when the user’s status is offline.
The offline/online statuses refer only to mobile apps and web portal and indicate when a user is logged in. Still you can call an offline user as the platform supports PUSH notifications and as long as he is connected to internet the call or chat will reach him.
Channels in common shows the list of channels shared by you and the user.
Starred messages group all the messages that you have marked as starred in this conversation.