Friend is offline

I can add the friend from that other profile, but it shows that friend offline (it is not offline or showing offline)

The problem is that the "Social and gaming" is limited. It is causing issues with finding friends (the all friends are offline issue), party's, joining games, etc.. The issue will hopefully be fixed soon! You can take a look at the issue here:
support.xbox.com/.../xbox-live-status

Hi, Currently Xbox is experiencing an outage that Xbox is working on fixing asap you can follow the updates on the website https://beta.support.xbox.com/xbox-live-status

If you select Alternate MAC address from the network settings you will have 2 options in the bottom left

Clear and Alternate MAC address

Select Clear unless you want to manually assign a new one. Clearing it automatically gives you a new one

Could you try the following ?

• Press the Home button so you're on the main page of the dashboard
  
• Press the Menu key right next to the home button and select
  Settings
• From the settings menu select Network and Advanced settings
  
• Select Alternate MAC address and Clear

You will now get a message saying you need to restart, just select restart