I was watching the CB 2.0 Tutorials - 21 - Integration with uddeIM Private Messaging video by Nick A. on Youtube:

In order to be able to send private message from someone else's profile it says we have to go to:
Community Builder: Plugin Management- Private Messaging System- Parameters tab
and selecting the option: PMS component TypeUddeIM 1.0 and 2.0+ or better
but I couldn't find the PMS component Type option in the Parameters tab (nor any of the other options that you can see on the video). I only have the Auto Delete option there so I can't send private messages from someone else's profile.

On the other hand, at the end of the video it goes to: Community Builder: Tab Management- Quick Message and publishes this option so it's supposed to be possible to send private message from the button in the Nested Tab Menu but this option didn't work to me because this option never appeared in this Nested Tab Menu.

I only have installed the UddeIm component (no modules or other UddeIm plugins) because Nick says you don't need to do it. Maybe it's a different version...

I would appreciate if someone can help me. What could be the problem?

I have the same issues and the same question. I want to use the Quick Message function, but none of the interfaces in my current CB/uddeIM installation (all current as of 28 November 2016) match those shown in the video.

Did you install and publish the Private Messaging plugin in CB?