They keep attacking random stuff.

Easy example: Prologue, everyone has puppet mode on, fight with 3 Mossfelds. I select opponent and choose attack, my main character attacks other (closer) target instead.

By AI mode off I mean "Puppet Mode" - I have it turned on for everyone and I turned off everything I could on "Behavior" list. Are there some more hidden AI options? I understand game isn't difficult, but I'd like more control over what is happening in combat.

Isn't the tutorial prologue a scripted fight? I'm not 100% certain, but I think it is.

No, it is just the earliest and most convenient moment to demonstrate.

Let's say you fight 2 enemies, enemy A and enemy B. Enemy A stands closer to you than B (who still stands in melee proximity). If character is ordered to attack enemy B, he will attack once and switch back to enemy A. Behavior is set to Puppet Mode.

Edit: Also when combat starts (enemy appear) characters throw away their heads and run to attack random targets instead of waiting for orders.

Ok, I'm going from memory again, since I haven't played this for ages. Have you made sure the party AI button (the one by the rest icon) is off. I think it's red for off, and blue for on? If puppet mode is working you will know, because they won't even follow you without orders.

Yes. Even more so, I went into behavior list of each party member and made sure that everything is switched off (Puppet Mode is "ON" of course).

Party follows just fine like in Baldur's Gate - you select all party members and click to point them where to go. It is just that every dialogue deselects all party members, but that's fine. When they are deselected, they don't follow.

Still there are some AI elements which are hideously active and turn fights into mess. Each fight is basically: party members go nuts, I click somewhere so they'd walk to chill down then select enemy target 1 by 1 (party attack like in BG/IWD doesn't work, at least not with AI off...) and watch party members attack whoever just happened to be closest to them (which happens to be all the enemies except the one I ordered to attack). *sigh*

Do you have Kaedrin's PrC mod installed?

I did after a recent fresh installation on a new PC. I had to uninstall it because the AI was totally wonked. I emailed him and he gave me a reply for something to try, but I can't remember his advice. Removed the mod and reinstated the original .tlk file and everything went back to only slightly stupid (Bioware default ;-) )

Nay, I played without any mods. I think this "AI is still partially ON when it is turned OFF" was exactly the reason why I couldn't get into this game first time around. I browsed whole internet on AI issue, found nothing useful, and simply gave up again.

Funny. I turned AI off and use strategy mode. Seems to work just fine.