I have to say that it's nice to know that we've jumped to #1 in score, although that is surely due to all the land and population we acquired from Rome. We can do better on the tech.
Military Tradition isn't a terrible choice. I didn't suggest a tech beyond Liberalism because I didn't realize we'd get there so fast!

We have to make sure that we have Gunpowder so that we can start building Cuirassiers, a good step up from Knights. Oh, and for Muskets. I also think that it would be a good time, well, soon, to switch to Nationalism for Drafting.
One thing I failed to consider is setting up a Globe Theatre city: A city with a huge food bonus that will allow near-constant drafting without a happiness penalty. We may want to convert one of our cities. Amsterdam could probably do, but we'll need Drama and several Theatres to unlock the National Wonder.
Just for clarification: Are we through the whole 30 turns, meaning that elections are upon us, or are there still some turns to go? Nevermind, I see that it was 15 turns.
The Ireland Issue: We should provide political asylum to Khan and any refugees who make it to our shores, but I think that it would be unwise to support the KRF in any capacity. Besides the risk that it will anger the Norse/Russian bloc, we will most likely be using up resources that would be better spent preparing for an all-out, conventional war. We will get revenge, but only when we can fight on
our terms.
Statehood: Assuming you mean "Vassal States," absolutely not. Assuming you mean "independent government," absolutely not. Allowing our provinces to fragment will only weaken us at a time when firm rule is most important.
Just a couple more notes, Lighthearter:
Birmingham needs to work the plains farms for the extra hammers, not the coastal tiles! Making sure that our Heroic Epic city is producing the most hammers possible is of CRITICAL importance. It's also hard to tell from the still screens, but is Birmingham working the mines I noted, too?
Also, Antium has one more hill that needs a mine.

Gotta maximize production in our military cities.
Nitpicks aside (though the Birmingham issue is a BIG one), it looks like you ran a very good set. Once all those Stock Exchanges finish (I forgot that they were our UB), we should be rolling in cash, relatively speaking (in practice, it just means we can afford to keep the tech slider higher). Meeting new people is probably nice. Hopefully some trade opportunities there. We'll probably want to get something better than Archers on the home island now that Russia/Vikings are our neighbors.

Anyway, overall, looks good.
Whoa we control Rome! Did I miss something?
Yes. At the start of my term, I successfully negotiated for Caesar's complete surrender and the annexation of remaining Roman territory.