There are probably other people who can lore post better than I can, but I'm a bit of a lore junkie myself so I can jump in on this one.
1) "Raen territory" is a bit of a misnomer. Unlike the xaela, the raen didn't strictly have territory of their own. Instead they were intermingled with the Doman and Hingans, and per the lore book many took up arms/worked under one or another lord in the Far East. Essentially unlike their xaela cousins, they integrated themselves with Doman and Hingan society. When Doma was razed those living there were just as affected by it as other Domans. Any raen who lived on the isle of Hingashi were unaffected by this since Hingashi is independent and Garlemald did not invade it.
While there are no solid numbers of refugees or any real information about racial distribution among them (even in the lore book), it can be presumed a good deal of the refugees were raen. That said there are many who yet stayed in the Far East, especially in smaller villages and farms and live under Garlean rule. There are more still who fled BEFORE the fires of war hit and made their homes elsewhere, at least one group in particular creating their own society in a...different and unexpected place altogether in the Far East (I'll avoid saying where for spoilers' sake).
2) The naming convention I'm not terribly solid on myself as they give enough information to go off of for naming an adventurer in the naming conventions but they didn't seem to account for roleplayers looking into doing something other than a combative character. One would assume it's something that could be stretched in the way you suggest though. (if any of the resident lore masters here can correct me on this if I'm wrong it would be appreciated though)
3) We know through the lorebook that the Doman refugees were refused at ports in both Hingashi and Thavnair before arriving in Thanalan. Hingashi was already entreating the Garleans as esteemed guests in the Hingan port of Kugane and they did not wish to bring the ire of the Garleans to bear on them by harboring refugees. Radz-at-Han in Thavnair similarly wanted nothing to do with them for the same reasons. Based on the route this suggests they took, a refugee in a capsized boat as your backstory suggests could have ended up literally anywhere in the southern regions of the world map, although if they were to end up in Eorzea it would be best to have them land somewhere on the southeastern coast of mainland Aldenard (the continent containing Thanalan, The Black Shroud, Coerthas, etc).
4) Yes, this was answered in point 1.
5) In the Far East, the raen are well-respected since a great number of them were very skilled warriors and loyal vassals. There are even some cases where raen established their own well-respected clans in the Doman tradition (this is observed as early as the Ninja 50-60 storyline). As far as Eorzea is concerned, while Yugiri hid her features for fear of startling Eorzean society, it was entirely unnecessary as it's made clear by the backstories of certain characters such as Sid from the Dark Knight storyline that Au Ra showed up in Eorzea probably within the last 10-20 years, but the problem was that they ran into the Ishgardians first. Ishgard, not knowing what to make of the scaled individuals, believed them to be heretics and dragonkin, and murdered them in droves. As of the present day though, the nature of the Auri people is better understood though the tension left over from the Ishgardians' wanton slaughter of the Au Ra has not been forgotten. Elsewise, they encounter the same welcome as any other race in Eorzea: Adventurers are welcoming of them due to the nature of their work, older individuals who have incredible pride in their homeland may yet carry some xenophobia about other races, but otherwise there is only casual racism thrown about here and there.
1) "Raen territory" is a bit of a misnomer. Unlike the xaela, the raen didn't strictly have territory of their own. Instead they were intermingled with the Doman and Hingans, and per the lore book many took up arms/worked under one or another lord in the Far East. Essentially unlike their xaela cousins, they integrated themselves with Doman and Hingan society. When Doma was razed those living there were just as affected by it as other Domans. Any raen who lived on the isle of Hingashi were unaffected by this since Hingashi is independent and Garlemald did not invade it.
While there are no solid numbers of refugees or any real information about racial distribution among them (even in the lore book), it can be presumed a good deal of the refugees were raen. That said there are many who yet stayed in the Far East, especially in smaller villages and farms and live under Garlean rule. There are more still who fled BEFORE the fires of war hit and made their homes elsewhere, at least one group in particular creating their own society in a...different and unexpected place altogether in the Far East (I'll avoid saying where for spoilers' sake).
2) The naming convention I'm not terribly solid on myself as they give enough information to go off of for naming an adventurer in the naming conventions but they didn't seem to account for roleplayers looking into doing something other than a combative character. One would assume it's something that could be stretched in the way you suggest though. (if any of the resident lore masters here can correct me on this if I'm wrong it would be appreciated though)
3) We know through the lorebook that the Doman refugees were refused at ports in both Hingashi and Thavnair before arriving in Thanalan. Hingashi was already entreating the Garleans as esteemed guests in the Hingan port of Kugane and they did not wish to bring the ire of the Garleans to bear on them by harboring refugees. Radz-at-Han in Thavnair similarly wanted nothing to do with them for the same reasons. Based on the route this suggests they took, a refugee in a capsized boat as your backstory suggests could have ended up literally anywhere in the southern regions of the world map, although if they were to end up in Eorzea it would be best to have them land somewhere on the southeastern coast of mainland Aldenard (the continent containing Thanalan, The Black Shroud, Coerthas, etc).
4) Yes, this was answered in point 1.
5) In the Far East, the raen are well-respected since a great number of them were very skilled warriors and loyal vassals. There are even some cases where raen established their own well-respected clans in the Doman tradition (this is observed as early as the Ninja 50-60 storyline). As far as Eorzea is concerned, while Yugiri hid her features for fear of startling Eorzean society, it was entirely unnecessary as it's made clear by the backstories of certain characters such as Sid from the Dark Knight storyline that Au Ra showed up in Eorzea probably within the last 10-20 years, but the problem was that they ran into the Ishgardians first. Ishgard, not knowing what to make of the scaled individuals, believed them to be heretics and dragonkin, and murdered them in droves. As of the present day though, the nature of the Auri people is better understood though the tension left over from the Ishgardians' wanton slaughter of the Au Ra has not been forgotten. Elsewise, they encounter the same welcome as any other race in Eorzea: Adventurers are welcoming of them due to the nature of their work, older individuals who have incredible pride in their homeland may yet carry some xenophobia about other races, but otherwise there is only casual racism thrown about here and there.