Egypt on the Earth map was the first game I played, too.
Looked at the save. Here's the basics of grand strategy that I think you need to know. The elements of success are lots of cities, in good locations, with high population, working lots of cottages. And lots of units, to keep from getting declared on and to take more cities. You need to have the most of that stuff to win. Good land means food resources, other resources, and floodplains/grasslands for cottages (in most cities) or hills for mines (in some cities). What you do with buildings is secondary.
Especially on lower levels you can win by expanding peacefully, building just enough units for defense, getting high population, and building a lot of cottages. You've pretty much done that, but it partly depends on your land. Persia's surroundings are only fair. Only your first seven cities were any good, except for Arbela which has very poor food. Sardis, ergili, tyre, pharsalos weren't worth settling. Meanwhile on this map Frederick is always the big dog. It's not a very balanced map. Frederick has a ton of excellent land that he can expand into easily. Asoka is small, but he has very good land. I think he has more cottages than you, which is why he's lower in score but more advanced in tech.
In general you have to look strategically at who has good land nearby that you can take, and who is powerful and needs to be taken down. That tells you who you attack.
> 1. I always try to out-culture my neighbors.
You only need enough culture to keep your fat cross in your possession.
> 2. I build cities to block neighor expansion even if it means leaving gaps
Fine, if they're going to be a rival. If they're not, it doesn't matter.
> 3. I always try to build all my cities in a balanced nature - rule #1 with me is build something first that will increase my city radius, then build culture-producing buildings that have secondary uses (i.e. library).
One or two culture buildings are enough.
You're building way too many buildings and not enough units. As to what buildings to build, I'm not sure where to begin.

All your national wonders are in terrible locations except Forbidden Palace and Heroic Epic, and your Heroic Epic city is building a completely useless cathedral instead of useful, Heroic Epic-bonused units. I can't even begin to describe how useless that cathedral is.
You might be able to take the game in the save to a cultural victory in the style of play that you like. Cultural victory uses a special but cookie-cutter strategy. Of the three cities that need legendary culture, in this case Susa would lag way behind Persepolis and Gordium. Cash-buy as many cathedrals in Susa as possible, run nothing but artists in any city and use all the great artists for great works in Susa (after settling one or two there), and turn the culture slider up all the way. That means no more research, so research assembly line first so that you can keep building infantry for defense. Get defensive pacts with Frederick and Asoka if possible.