I took a look at your save.
your citie placement seems ok.
you have a lot of undeveloped land, you need a lot more workers. you only have 11 now, and they can't keep up. so you need more. Best would be to double them and pair them up. each pair working to improve 1 city.
Your running caste system, while you only have 2 specialist. It would be better to run slavery to build up your cities.
Your cities itself ar really underdeveloped. Your at 1600 and yoiu still haven't build graneries and markets. its no wonder your economy is in shambles. the good thing is that they at least have a library.
You didn't research machinery/enginering/guilds and banking. Why? machinery will help with production and growth for your grassland hills with windmills.
Enginering will help you move your troops quicker on roads.
Banking and guilds will help your economy.
Berlin is running a priest. Why? its better to put him in the field helping growing the citie.
Hamburg is building the forbidden palace while it doesnt have the basic buildings like granary, market. and it is to close to your capitol to have the forbidden palace.
Munich needs chain iragation to help the citie grow, and work al its tiles.
Cologne needs a few more farms to grow to full size while still working those mines.
Frankfurt needs more farms, to reach its full potential, and is a much better place for the forbidden palace. its on the other end of your empire.
gordium is working plain towns, those plains should be farmed, and the grassland tiles should be towns. its building the versaille, while the citie itself is undeveloped.
arbela is working lots of unimproved tiles.
parsagarde same as arbela.
All your cities don't have graneries and markets. you really need to build those if you want your cities and empire to grow.
I think the main problem for you to strugle so much, is that you don't develop your cities fast enough. graneries you should have as 1 of your first builds in new cities. then libraries (alfabet comes earlier than currency) or markets and courthouses. if you do it right, you should have some cities before 1AD with at least markets/libraries and a granery. wich should help you support a growing empire.
as for your war with the romans, I think you need more units or upgrade your axeman to maceman. (wich I think you can't cause you don't have machinerie)
Maybey you can take some cities of them, but your up against longbowman, wich you need maceman and trebuchets (enginering) for.
But keep it up. Its good to know you won't quit.

Improve your cities and land earlier and you won't have any problems keeping up and beating the ai.
Soon it will be tanks vs longbowman.
