Having played Arena, I am aware of most of the lore about Jagar Tharn was created after the game in which he actually played a major role was released. I have several questions about him. First, what was his race?
Half-breed.
"
Part Dark Elf, part High Elf, and part the gods only know what. All the worst qualities of all his combined bloods..." - "The Real Barenziah".
Also, who are Imperials descended from? Are Imperials a mix of several different races?
Nords + Bretons + lot of different separate Nedic tribes + even Akaviri sometimes.
Also, I remember Jauffre stating Mehrunes Dagon assisted Tharn. How did Dagon assist Tharn, with servants and/or use of his realm to serve as a prison for Emperor Uriel Septim VII or something else?
The story of Battlespire is about pact of Tharn and Mechrunes.
The inprisonment of Uriel in Mechrunes realm is possible, but I think it was a clother to Camoran's Paradise inner-Realm.
From background stories in Daggerfall, I'm assuming people were aware of Tharn controlling the Empire and from those stories, I'm assuming Tharn held an iron grip over the empire, but are either of those statements true?
Opposite. Tharn didn't rule Empire at all, and this caused numerous wars and rebellions. Moreover, it seems that Tharn even sectretly supported this conflicts.
Was Tharn's rule a time of fear and oppression?
Time of fear and lawlessness, to be correct.
As for my final topic, since it seems the lore from Arena(and even Daggerfall, in some cases) is outdated, are we to assume that what we saw in Arena is not canon?
No. Arena lore should not be non-canon; but it should be interpreted keeping in mind more recent lore.
Can we assume the Imperial City resembled its most recent form shown in Oblivion during Tharn's rule instead of its form shown in Arena?
Yes.
White Gold Tower's presence in Oblivion but absence in Arena seems to confirm that, but I just needed to make sure Talos didn't decide to redesign the Imperial City along with the jungles of Cyrodiil.
If Talos did, if would have effect on PGE description of IC, not on Arena depiction.
Did Emperor Uriel Septim VII and many citizens of the Empire really speak with generic, medieval accents at one point?
It's possible...
Could The Eternal Champion, while possibly not being an Argonian, really survive Black Marsh?
He's Eternal Champion, after all.