I'll look at both saves (860 and 1645), but I'm relatively new to Regent as well ....
Oh wow. Okay, starting with the 860:
First, you're building two wonders with 185 turns to go on each. Bad move. You're throwing away most of those shields when you could be building soldiers (to kill things) or Workers/Settlers.
Second, you don't have enough Workers. As a non-Industrial Civ, you want at least two Workers/City (Slaves count as half a Worker, but I didn't count them) - you had 7 workers and ... what, five cities?
Third: Cathedral is a no-no. You shouldn't need it - either keep the population down, get more Luxuries, or change the Lux Slider. Preferably the latter two, as they're going to be more helpful when you finally get out of Despotism.
About here, I Retired the game and watched the Replay:
It's been said before: You *NEED* to expand. Berlin is sitting on a Floodplains hotspot - there are four Wheat-Floodplains in its city radius and three Bonus Grasslands (which, in the 1645 save, were Irrigated - they should've been mined). Those Persian cities to the north of Berlin never should've gotten placed there. You could've split those four Wheats among three cities.
Likewise, Zorak, Dakyunus, and Borazjan should never have been open for the Persians to settle. As you may have noticed later, they cut your empire in half, and situated on Hills, they're *very* tough nuts to crack.
During and after the war with Sumeria, you should have been cranking out Settlers to take all those empty spots to the east and south. For that matter, who keeps destroying cities? If possible, you should keep them.
As an example of how slowly you were expanding, after destroying Sumeria (IIRC), you had four cities - three in the north and one in the south. The Persians had 8, and the Spanish 6. After founding Kongisburg, your fifth city, the Persians had 13 cities, and the Spanish 9. You *need* to expand more quickly; even if you don't want the cities in and of themselves, they'll boost your income and unit support, and deny the AI those cities.
Moving on to 1645:
Again, you don't have enough Workers, and you have a larger empire to worry about now.
Colloseums and Cathedrals should not be built.
Why, exactly, are you importing Furs from Persia? You have your own source (near Murcia), and can cancel the deal whenever you want, as it's expired.
Finally, a couple things I noted for reference:
When you go to war with Persia, the first cities you need to take are going to be Istakhr and Zohak, as they divide your empire. In order to do that (and in general), you're going to need Cannons. Lots of them. Bombard and redline every unit in the city before attacking.
After that, your worries will be Borazjan, Dakyunus, Jinjan, Altin Tepe, and Leipzig. If you can take those cities without losing many/any of your own, the Persians should be willing to make Peace.
Lastly: Turn the "Always Wait at End of Turn" option on in the Preferences. When units go zipping around the screen (auto-move?) and the turn ends before you can check things out, bad things pile up.
I'll try to run the 860 save up to 1645 some time this weekend, see how I do. If I can get around to it, I'll post the save here.