Hello, Yury!
First of all, thank you very much for such detailed response. Unfortunately, at the moment I can't give you all answers cause I am far away from my demo installation and have remote access only.
So, what I can say right now?
My primary task is to change autorization portal from Fortigate's to Extreme NAC's and it's almost done. There are a few interface things which still unclear, but I hope we'll solve them=)
Then, I want to make NAC to make lookups to my LDAP (Active Directory). And it's done.
I can say that two things above work in connection, but not 100% correct.
Details:
After connection to SSID is established, I try to open any website in browser and get to NAC's portal page.
There is a question:
https://nac/main - is it correct URL for redirection? Cause I've set exactly this page...
Regardless correct it or not, on a client side I see this (everything below demostrated for wired client, but from a wireless client I see the same):

(Black text on foreground is a disgusting thing - I don't know now to remove that)
So, If I input wrong password I get:

If I enter correct login/password I get:

After I tick "Agree" and click "Complete registration" I get endless "Network Registration in Progress..."

There are my questions:
1) Actually, I want just to give users Internet access after successful login without any "Policy Acceptance" - let they get a page they have requested. How can I get that?
2) How can I remove black text in foreground "You have been denied network access because your device is not currently registered to the network. bla-bla-bla..."?
3) Are there any ways to make NAC's portal page appear automatically without manual browser opening by user? Like in 100% airports and hotels are...?
Many thanks to you, Yury...