Nice research Galin.
As Tolkien wrote the books the stories and ideas evolved over time. It is difficult to determine the precise origins of orcs from these texts due to this evolution. However, surely logic should prevail? (...) Surely then, using that argument alone, Melkor could not have created orcs and trolls from lifeless material if they were not to be just mindless puppets under his direct control.
External chronology reveals the early 'phase' in which Morgoth can seemingly make creatures like Orcs and Balrogs without needing to corrupt some other living beings -- and also reveals a time when Tolkien surely revises this. The older phase lasts up until... let's say the early 1950s for ease of reference.
This date ignores Frodo's statement in The Lord of the Rings for example, and not just because I can't seem to date it very easily, but because after The Lord of the Rings was written, Tolkien appears to have revisited his Silmarillion writings by initially restating that Morgoth simply 'made' Orcs in the same general way as he had in the 1930s.
So generally speaking, for decades, and up until the early 1950s, Tolkien believed Morgoth could create orcs out of things like stone and hatred, and create Balrogs too. But what about Dwarves?
In the 1930s we find the emergence (in The Annals of Beleriand) of the legend of Aule making the Dwarves, but interestingly, at this point the Dwarves have 'no spirit indwelling' and they have skill but not art.
No spirit indwelling? Hmm. In any case Tolkien would change this so that the Noldor believed the Dwarves had no indwelling spirit, and thus they had skill but not art, adding that they believed the Dwarves go back into the stone of the mountains of which they were made.
And jumping over to the Silmarillion of the mid to later 1930s, there is it noted:
'Wherefore the Dwarfs are like the Orcs in this: that they come from the wilfulness of one of the Valar; but they were not made out of malice and mockery, and were not begotten of evil purpose. Yet they derive their thought and being after their measure from only one of the Powers, whereas Elves and Men, to whomsoever among the Valar they chiefly turn, have kinship with all in some degree.'
So however this works in more detail, this was the notion 'paired' (in a sense) with Morgoth creating Orcs out of stone and hatred. And it was once again not until the 1950s that we find the text in which Aule now creates 'puppets' and Eru gives the Dwarves independent life and wills (as chosen for the 1977 Silmarillion by Christopher Tolkien of course).
And yes Tolkien wrote 'Dwarfs' there
The ultimate point here is that the pre-1950s idea had been revised by JRRT, but Christopher Tolkien still had a number of choices before him once the revision had been made (and 'puppets' may have lingered as an alternate kind of making for some things, again in the early 1950s at least).
So Orcs must now be corruptions of something. But what?
It could be argued that orcs and trolls only functioned when controlled by a greater power, but in my opinion the orcish armies falling into disarray when Melkor/Sauron were defeated was more a matter of having lost their leadership they no longer followed their orders and sank into unorganised squabbling and infighting. This is different to becoming mindless puppets as Aule's dwarves would have been.
There is also a distinction Tolkien makes about servitude and domination. JRRT agrees that Orcs were not puppets but some were so dominated by Morgoth's will that they seemed to be puppet like. This was more along the lines of (as Tolkien described): '... servitude to a central will that reduced the Orcs almost to an ant-like life...'.
To me, this logic implies, whether it is written or not, that Melkor must have corrupted something already living to make the orcs rather than just creating them himself.
You are correct, and it is written, but again it's not simply logic but also following the external chronology to the point when JRRT certainly changes his mind about 'making', and the old concept gives way to the new. And I don't think there was any question in Christopher Tolkien's mind that he [Christopher Tolkien] would reject the old idea for the 1977 Silmarillion.
The question then becomes, what did he corrupt to make the orcs? I had always thought Elves. There is the argument, however, that if he created them from Elves, wouldn't orcs be immortal? Not necessarily. When he spread his essence through Middle Earth as Morgoth's Ring, the effect was corrosive over time on the Elves. They grew weary, tired and began to fade. If his diffused essence had that power, surely he had the power to corrupt the immortal bodies of his orcs into mortal ones. Maybe all that twisting and corruption of their flesh made their bodies mortal, leaving their fea to go to the Halls of Mandos once they died?
What we can say is that the 'immortality question' was one Tolkien posed to himself. And I think it shows that he found the matter somewhat problematic. Tolkien noted (text VIII):
'It also seems clear (...) that though Melkor could utterly corrupt and ruin individuals, it is not possible to contemplate his absolute perversion of a whole people, or group of peoples, and his making that state heritable. [added later: The latter must (if a fact) be an act of Eru.]'
'In that case Elves, as a source, are very unlikely. And are Orcs 'immortal' in the Elvish sense? Or Trolls? (...)'
JRRT, Myths Transformed, Morgoth's Ring
So here we have two concerns: immortality, and the possibility of Morgoth not just corrupting beings, but making this corruption a heritable state -- in other words (as I read this), what will the children be if corrupted Elves [who have become Orcs] breed? Elves or Orcs? If Orcs, Morgoth has made his corruption a heritable state, and if this is true, Elves seem an unlikely source to JRRT himself (or at least this seems part of the reason anyway).
Men would solve the immortality question, at least. And there might be other concerns. As noted above, Morgoth could so dominate some Orcs that they seemed like 'puppets' with no will of their own, some even slaying themselves when the Dark Lord was defeated, for example. And in a late note Tolkien explained...
'Other originally independent creatures, and Men among them (but neither Elves nor Dwarves), could also be reduced to a like condition.'
JRRT, late note attached to text X 'Orcs from Men'
If Orcs could be so dominated, it makes sense (to me anyway) that the source for Orcs could be so dominated as well, but here it's said that neither Elves nor Dwarves could be reduced to such a notable condition. One could argue that once Elves became Orcs they could be 'absorbed' in this way, but I also think that Men were -- generally speaking now -- more easily swayed to the will of the Dark Lords.
Tolkien even notes, in text X [he had adjusted the chronology to allow for Men to be the source for Orcs, although admitted that it was still not without its difficulties]:
'This view of the origin of orcs thus meets with difficulties of chronology. But though Men may take comfort in this, the theory remains nonetheless the most probable. It accords with all that is known of Melkor, and of the nature and behaviour of Orcs -- and Men.'
In my opinion, in general Men were already 'closer' to Orcs than Elves were, and notably I think, Men could be found in Morgoth's forces as well as Sauron's. Not all Men of course! But again, in general.
Someone posted above that orcs were possibly made from corrupted Men. My memory's failing me, but weren't orcs around before Men awoke? If Melkor had stumbled upon them before they awoke and corrupted them, wouldn't he have corrupted them all? In that case there would have been no Men. I personally don't think Men were involved until Saruman possibly crossed orcs with Men to create Uruk-hai.
I appreciate your 'possibly' here, concerning the Uruk-hai
And as I say, Tolkien adjusted the chronology to make Men a possible source for Orcs, even though this new chronology was not wholly without its difficulties. And there would be some even earlier Orcs as well, considering the corrupted Maiar.
I won't go into the 'beast section' of your post here, as that alone raises a number of questions and this post is probably quite long by now!