I have few questions to experienced players...
For start:

1. Manamune and Archangel Stuff - those items has similiar Unique Passives. But will they work together? I mean - Can I get 1000 Mana by casting with AS and 1000 Mana by auto attack with Manamune? Or It would be only once 1k Mana Bonus?

2. Is there any list of Auras Range? I think i found sth like that long time ago, but I'm not sure...

the tear of the goddess is a seperate bonus pool shared by all 3 items, you only get 1 charge regardless. however on the flip side you can charge your tear up and when you upgrade it the bonus pool is still charged just as high as you left it. once you hit 1k bonus you cant go higher no matter what you have.

not sure on the aura ranges, they are pretty huge, something like 800ish

So, It's only 1k Mana Bonus but - From this 1000 Mana Points i have still converted 2% for AD and 3% for AP ( Im building those two on Nunu somethimes )

About Aura range - Im thinking if Soraka's "Q" and Nunu's ulti will work 100% effective with Abyssal Scepter. I don't know if aura and skill range are the same...

Seach each aura you want here. They have the estimated range.

No, "unique" passives will not stack on with the same item...For example, you can buy six Deathcaps if you so chose, but you only get the % boost off of one (however, that still means each Deathcap would add 182 rather than the 140, ya' follow?)

you seem to have a good understanding and what the people have said above is correct, but if your still not sure heres something to help clear it up even more

when a lower teir item has a unique ability, this ability will be shared between all the items it builds into. even if the ability changes slightly. such as sheen. trinity force and lich bane has different values than each other and sheen, but the ability it does is still the same. so having any combination of the 3, you'll only get 1 effect out of it. I cant remember which one will apply but ya you only get 1.

so for tears of the goddess, you only get the 1 ability. even though archangel and manamune has 2 different ways of building it.

hope this clears up any questions you have about this item, and any future questions about similar situations