This definitely looks like some hardware problem, but I'd like to know what.
I've installed Yosemite and now there are some changes.
When no externals are connected:
Instead of simple freezing, now it freezes and couple of seconds later turns off. But, it no longer runs fine via charger when battery is at 100%. Instead, it froze-shut off after 38 minutes. Then, I unhook it from charger and tried it off of battery, where it ran fine till it dropped to 77% after 58 minutes (of mostly torture, to speed up battery drain) and then it started randomly turning off. Every time I start it up again, it stays on for a shorter period of time, unless I let it sit off a bit. Then it "normalizes"
When FireWire HDD is connected:
Works flawlessly. Either battery or power adapter. Currently non stop working for over 15hrs without a hitch.
When it shutdown after first freeze in Yosemite, I've started digging up info on that and came to conclusion that SMC update should resolve it. So I tried it again and now SUCCESS. Also, I've never seen any update being done as fast as this. Preparing was typical (maybe around 30s), but actual update after restart, 1-2s max.
SMC firmware is now 2.2f44, but the problem persists.
I've reset SMC and PRAM again, but no change.
Noticed in Console "last shutdown cause" immediately after those random shutdowns: 5, 0 and finally -128. Although -128 is one when it started turning off quicker, both 5 and 0 coincide with freeze-shutdown. I've found that 5 and 0 are normal shutdown codes, but I don't see anything normal with what happened.
Also, I've noticed that computer fan is quite lazy. While stressing, GPU temp reached 90C, yet fan only slowly started speeding up reaching "blazing" speed of 2200rpm. I know fan works because it speeds up to full speed in ASD tests.
Now I decided to put ASD on internal HDD and boot it from there without any externals to see if any error appears. If it passes all tests (I've put it to do a loop of 3 passes in ASD OS), I'll do a bit of "transplanting", taking the logic board to a different case.
Will update with new info.
All suggestions are welcome.
Notice, there are no "apple geniuses" in my country, only guys with screwdrivers and soldering irons.
