Shutting X server down causes WiFi to disconnect
 

How can i make ubuntu not disconnect from wifi and in fact not depend on X server when managing network?

Networking does not need X at all.

You should set up your networking details in the file /etc/network/interfaces
See man interfaces for the details.

Yes, i know this. But the problem is real. Though, i have found its reason: on X shutdown nm-applet gets SIGHUP or some other signal, and disconnects from network and quits. nohup doesn't help. How can i make it not disconnect?

Instead of using "network manager" to establish the connection, configure your /etc/network/interfaces file to do the work for you. Here's the part of mine that refers to my wireless interface which is eth1 :
My connection comes up at boot, and stays up until I turn the PC off.
Nobody needs to be logged in, and I don't need X running.

See man interfaces or the many guides on the web.

I would do this (or something similar) on my LFS machine, but on Ubuntu i'd like to use some GUI way to do this :) Is there any?

Sure, there's NM or (better) wicd

But as you have discovered, the GUI needs X and gets killed when you logout, so the connection is lost and you are back at post #1

Why do I think we are going round in circles here?

Because you assume i need a GUI daemon like network-manager while i just need a GUI front-end to /etc/network/interfaces.
Anyway, as i have searched, there don't appear to exist such front-ends, so i have configured interfaces manually.