2 more turns played and I have great news.
First, the settler is almost in the desired spot and no CS unit or barb unit decided to mess with our pathing. That can be a huge problem. In Civ 5 PBEM 5, I lost like 3 turns or something in my second city plant due to a single barb unit that refused to cooperate. I decided to keep the slonger near the Capital to protect the next settler. This is to be 100% sure nothing bad will happen, but I don't think anything would happen if I just kept moving him.
Anyway, the plan is to move the warrior near the barb camp after second city is settled. The warrior needs to soften up a unit, if we want the slinger to kill it. The slinger will walk the initial path with the second settler, and we meet them halfway, with the warrior escorting the settler for the second part, while the slinger finishes the barb. That's the plan, at least.
Anyway, notice that the Capital grabbed another tile, opening up the wheat to be bought. The tile picker shows that another second ring hill would be picked, over the third ring wheat. I guess we'll need to buy our food.
But the main thing, already spoiled in the first screenshot if you look carefully, is that we found a second continent. Not only did it boost Foreign Trade, but it gave us a envoy in Cultural CS Kumasi. It's not showing in the interface yet, but are actually making 4.8 culture per turn now.
As you can see, I decided to be stubborn and kept going northeast, mainly because I didn't want to lose a full turn of scouting just to traverse the river. The new continent ended up being just a bit ahead, in what is some awkward frontiers... Pretty good land in this parts of the map, I have to say.
Last turn, I changed from Archery to BW, since we were very close to 50% done. I'm really not sure where to go next with tech. I chose BW because it's a tech we'll definetely want pretty early in the game, but I think we need to wait for an Eureka here too, so I'm not sure we'll be finishing it soon. I don't want to tech masonry, because I don't want CSs to get walls.
There's Currency outside of this screenshot, that is a pretty good tech on the way to Apprenticeship. A TR is something we should consider building, but right now I think our hands are a bit tied with the military plans. I guess we can just keep teching less than 50% of the tech costs, while we wait for the Eurekas. Anyway, I think the Archery Eureka is the main one, if we get there, we open up Horseback Riding, which we already Eureka'ed. Not that HBR will help us without Encampments, since we only have 1 horse... Anyway, we need to think about what to tech next.
On the culture department, I think we finish Foreign Trade (even though we have no policy switch to make) and we keep going to Early Empire for the settler policy card. I think we'll have 6 pop in time, but we can always make a change to another civic, if that's not the case. The big question regarding Civics always comes after Political Philosophy, so until then I think it'll be pretty straightforward.
Finally, some strategic view screenshots, as asked by Pindicator:
East of the Capital:
East of Geneva and Kumasi:
Second city area and Yerevan:
West of the Capital: