Last Exile: Fam, The Silver Wing/WMG

Fam really IS a Princess.

Just throwing this in, since the second series is just beginning, but that throwaway line by Giselle (highlighted in the *exact* same way in the manga) sounds suspiciously like a plot point... or a red herring.

While not an actual princess, evidence has gradually accumulated over the course of the series that Fam is actually nobility, if the theory (listed in one of the lower entries) that she is General Sadri's lost granddaughter is confirmed.
Confirmed, though not the princess part.

Claus and Lavie won't appear in Fam: The Silver Wing.

They didn't appear in the OP. Pretty much Gonzo's style is to show off all the important people in the OP, making it total spoilers.

There's mention of a Grand Race. While there's nothing in the OP of them, the even is as good a chance as any for a cameo.
They finally appeared in the 2nd recap episode with some new scenes.

The Guild, or a splinter faction of the Guild, is yet again manipulating events to its own ends.

While the Ades Federation seems to have a very good reason to go to war against its neighbors, it just bothers me just how convenient an excuse it is, ESPECIALLY since some of the generals themselves comment on how the king of Turan was a moderate, which means he would have been likely accepted a more peaceful means of ending the conflict. Then there's the mention of the already limited resources of the planet, and how there's really not enough to go around... Hmm.

My guess? Someone is manipulating the war to prune the excess population. Given what happened in the previous series, it's easy to think of the Guild, or at least the Terran equivalent, as once again knee-deep in this again, as all it takes is an extremist (like Delphine) to twist its mandate. And what if it's mandate is keeping the resources of the planet at a sustainable level? If the level somehow affected by the arrival of more people than the planet can currently support, then why not just get rid of all those people who're causing the imbalance?

OP here again, Chapter 1 of the bridge manga Sunadoke no Tabibito/Travelers from the Hourglass practically confirm that the Guild is up to no good again: [1].

Dio and the Silvius are scouts for Empress Sophia and the cast of Last Exile

The Silvius looks, flies, and is crewed like the Silvana (right up to being commanded by Tatianna), except for the whole "putting the 'ship' back in 'airship'" bit. It appeared two years prior to events. Dio joined the Sky Pirates six months prior to events. Dio knows an awful lot about how the Silvius operates (plus he flat-out called it a scoutship), and even mentioned having permission from Sophia in Episode 2. And we know that this planet's biggest problem is Exiles bringing back colonists to take land from the current inhabitants (as the Ades Federation puts it, anyway).

Conclusion? After taming the Exile on Planet Prester, Sophia and company decided to come home. But not being dumb about it, they sent in an advance scout to figure out the landscape, who concluded that it'll take some time until they're ready. Dio, being Dio, did things a bit differently, leaving the Silvius to go at the problem from another angle.

And the series will end (or perhaps reach a midpoint) with the Prester Exile showing up with Sophia, Al, and maybe even Claus and Lavie after all.

Judging by the map in the 8'th episode, Anatoray already has its own territory on the planet, to the southeast of Gracies. It's just that it's rather isolated and isn't much involved into the overall global politics, just like its northern neighbour. Othervise your ideas are essentially confirmed as of now.

Farahnāz was assassinated.

So far there have been some hints that Empress Farahnāz wanted a peaceful solution to the problems caused by the returning Exiles. She may have been assassinated by by those who disagreed with her, so that her daughter Sara could be raised to lead the assassins genocide campaign against the other nations.

Farahnāz was indeed assassinated but not by her followers but by Exiles who wanted revenge for deaths of their people before the peace treaty and Grand Race.

When Claus and Lavie finally appear on Sliver Wing, the audience will find out that Claus and Tatiana are already a couple!

Thinks about it, the Last Exile: Travelers from the Hourglass manga has been showing Tatiana's feelings for Claus, the Ship Tease between the two and Alister shipping them. By the end of the Travelers from the Hourglass manga Claus falls in love with Tatiana and both of them become a couple.
- Claus and Lavie finally appeared in a cameo in Sliver Wing but the current relationship between Claus and Tatiana has yet to be told which the Travelers from the Hourglass manga may explain whether they became a couple or not.

Fam and General Sadri are related.

Might be a bit of a stretch at this point, but both Fam and General Sadri share eye colors. Incidentally, during episode 11, the latter is seen looking at a picture in his locket, generally assumed to be his daughter [2]. She looks incredibly similar to the woman shown clutching Fam as a baby when she was recovered by Atamora [3]. It might just be a case of limited designs for the background characters, but it's something to be noted.

This doesn't explain why Fam was discovered with a medallion containing what looks like a Guild emblem [4], though if it's true that General Sadri isn't an Ades native like General Vasant, then like in the case of the Turanian princesses, Guild blood had intermingled in the family tree in the past... And if the family was considered nobility, well, it segues well with the first WMG on this page.

All-but confirmed as of Episode 17[5]^{[dead link]}. The first time Fam and Sadri meets, Fam reminds Sadri of a young girl who looks like her.
This theory is about to be confirmed. In Episode 18, Sadri takes Fam for a dance and asks about her parents and family to see if they are related.
Episode 20 pretty much hammers the hints over the viewer's heads, particularly during a flashback where we see Raha and Sadri argue over Ades' policies.
Confirmed finally in the last episode.