When a Mangekyou Sharingan is replaced with someone else's eyes in an attempt to obtain Eternal Mangekyou Sharingan, do the eyes retain the host's powers or the donor's Ocular powers? Also, why can a "sealed Sharingan" merge to form an Eternal Mangekyou?
They probably keep the powers of the previous host.
From the wiki:
Although these eyes merge the designs of the two Uchiha's Mangekyō Sharingan, they're still the eyes of the previous owner and thus react to certain techniques that are aimed at the original owner's Mangekyō Sharingan.
However, we've only seen two Eternal Sharingans, on Madara and Sasuke. We do not know the eye powers of Madara's brother, and Sasuke and Itachi had the same powers, so we cannot infer solely from manga that the original host keeps his powers.
In Sasuke's case, He kept his own powers, so its most likely the case that the wielder keeps their own powers.
Itachi's powers were Amaterasu and Tsukuyomi. Sasuke's powers are Amaterasu and an unamed power I will call Amaterasu Control that let him control Amaterasu as if it was Gaara's sand, and put the inextinguishable flames out at will. We see this power clearly in that Itachi only ever shot Amaterasu out like a gun from his eye, hitting whatever he was looking at. We see Sasuke not only do the same, but also put out the flames and shape them, such as into spikes, on his own hands like Chidori, or even to coat Susanoo in them and create a shield so that they spread to the attacker.
After Sasuke obtained the EMS, he still used Amaterasu control to the same degree, but he never used Tsukuyomi because he couldn't. In Chapter 585, during Sasuke's fight against Kabuto,
he and the Reanimated Itachi cast genjutsu on eachother to break out of Kabuto's Genjutsu. Itachi used Tsukuyomi, while Sasuke used regular Sharingan genjutsu.
If Sasuke was able to use Tsukuyomi, that would have been the time to use it, but he didn't. Instead he keeps on using Amaterasu Control for precisions attacks using Amaterasu. The best example I can think off right now, In his Final fight in the main series
against Naruto, Sasuke uses Universal Pull to bring in Naruto and his few Shadow clones, and then surrounds himself in Amaterasu flames. Then he creates spikes around his whole body made of the black flame just before Naruto and his clones reach Him, piercing all the shadow clones, and Naruto barely dodges by using his Chakra cloak to grab onto the flames.
TL;DR he still uses Amaterasu Control after obtaining the EMS, but genjutsu wise only ever uses Sharingan Genjutsu. Thus the most likely answer is that they keep their origional powers. The unique special powers of the other individual are most likely lost, replaced with the other perks EMS has.