1. You seem to have had too few soldiers. I was guilty of that for most of my games, and I still am partially guilty.
I keep trying to tell myself that a living civilization which has philosophy in 1 CE is better than a dead one which had philosophy in 500 BCE.
(randomly chosen tech)
To address this, the best advice I've received is this: designate a production city, make it one of the first cities you settle. None of your neighbours are early warmonger, as best I know, so you don't need to make this your second or third city either, but don't forget it.
2. In the same idea as the first point, you need to specialize cities. Obviously, this can't be done for most cities, as few spots are great city spots, but you need at least some specialized cities.
- production city - settle early - lots of hills and enough food are a desirable; a river might be nice for later as well
- gp farm - a lot of food - this city will work the food heavy tiles and employ a lot of specialists otherwise; you usually want mostly scientist specialists unless you want to try a more specific strategy
- one or more commerce cities - these will work cottages and luxury resources; on this particular map, Rome is the best commerce city you'll have for a long time
Try to build these, and mainly these: (i.e. weigh in the benefits vs costs for other buildings; don't overbuild - also, these are relevant to the early game; ask again after you reach middle game and I'll try to complete the list
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- granary in most cities
- libraries in commerce cities and in cities where you employ scientists; definitely in Rome on this map and in the GP farm; also, you need at least 6 for reasons you'll understand in the Renaissance
- forges in production cities
- baracks in production cities
A special case could be made for markets in your commerce cities. The Roman UB is the forum, which replaces the market and offers 25% more GPP, so you also want to build it in your GP farm.
After that, the only job of the production cities will be to train soldiers. But don't train warriors just for respecting this rule, for instance.
You can make an occasional exception to train workers and settlers, but you mostly want production cities to help your armies
If you have currency and/or alphabet, whenever a city can't build something of its specialization, build wealth/research. Exceptions to this are to be made when in war and you need troops.
Please note that these advices so far aren't complete, but I want to emphasize that two great problems I've faced, and many other seem to have faced, are overbuilding and not specializing. A military city will never use a library, a commerce city will never use a barracks and so on.
Also, try to have about 1.5 workers / city.
Last thing, since you lost due to war, you should know something about your neighbours:
Willem, Zara and Huyana all attack even if they're pleased with you. Try to get at least one of them to be friendly to you. If you have extra resources which they don't, don't be shy to gift them the surplus, which offers +1 and then +2 diplo bonus after some turns. Try to be in the same religion as some of them. Try to honour their requests for gifts and remember that you can also ask for gifts every 30ish turns. (Never ask for tribute from someone you want to be friends with) Have open borders with them.
Obviously, diplo isn't so easy, but those will do.
And another specific advice to this map, and usually to watery maps with many islands: try to get the GLh. Don't sacrifice too much for it, but try to make it a priority. Also, Rome is greatly placed, has enough production and the leader is Ind. It's easier to get the GLh on this map.