Blackhand is power-hungry and bloodthirsty, Drunk on the Dark Side before he even takes the Fel. But he is still very traditional and has an honor that Gul'dan hasn't quite been able to get rid of. In this way, he represents the corrupted orcs perfectly.
Related to the above, Gul'dan is the one orc who doesn't think like an orc. He has no honor, no care for tradition, and a lust for demonic power that led to him personally ripping a hole to another world. This is why he needs Blackhand—as seen when Blackhand dies, the Horde would never directly follow someone who acts in such an alien manner. In the original canon, this is why Gul'dan's warlocks ruled secretly as the Shadow Council, with Blackhand officially occupying the post of Warchief.
Saving a baby's life might seem a bit out of character for someone like Gul'dan, but it did serve as an impressive demonstration of the power of fel magic. It also serves as PR for Gul'dan, portraying him as a fatherly leader. He also says that the baby is another warrior for the Horde. How right and wrong he is.
Moreover, even if he didn't give a damn about the baby's life, the baby's death was something he really couldn't allow to stand. Gul'dan's leadership predicates on his promises of a healthy new world for orc-kind to claim, so having the first orc born there - a respected chief's son, hence an infant expected to be strong and hardy - die without even taking a breath, could have been taken for a terrible omen: a sign that this new land, despite its lush appearance, wasn't fit for the orc clans to live and breed in. Furthermore, if word of Draka's transit-induced stillbirth made it back through the Dark Portal, any expectant parents among the waiting Horde's ranks would likely refuse to cross over until after their own young were safely born, delaying much of the invading force's arrival by months and impeding Gul'dan's conquests.
During one instance of Translation Convention, while Durotan presents his case to King Llane, Garona can be heard in the background translating his orcish dialogue, and she's clearly not speaking English. This makes perfect sense, considering that Azeroth and its history have nothing to do with Earth - of course they wouldn't speak English there. This is something that dates back to WoW's early days, if not before.
Garona having green skin may count as Fridge Foreshadowing. We never see any indication of Gul'dan using Fel magic on her, implying that she may have had the green skin that marks her as having been touched by the Fel from birth. And Medivh, who is concealing that he's been corrupted for quite a long while (whether he had the game timeline's problem of getting possessed while still in his mother's womb or just made inadvisable use of Black Magic), hints to her that he is her father.
Blackhand invoking Mak'gora on Lothar makes some sense: As much as the Warchief is the leader of the Horde, he is in charge of a warband of warriors that honor and respect strength and prowess. Blackhand, for all his leadership, has had very few victories to his name (if any), and what we have seen on-screen shows that he's been getting his ass handed to him, no pun intended. The one victory he can claim is that he killed the son of the small-teeth's champion, which isn't much. At the same time, at the final battle with the small-teeth, he was denied the honor of killing Llane, their chieftain. So Blackhand honestly needs a victory he can solidly claim as his own. If the chieftain is dead, then their champion will be sufficient, especially after Lothar came riding in hard and took out a good number of warriors with his gryphon.
In the climax, when Medivh's fel corruption takes over his body, he grows massively in size and grows horns. If you know the lore, that may very well have been the spirit of Sargeras trying to take complete control over him.
If Khadgar hadn't cast that shield spell in the forest when he did, Durotan would have killed him.
