OK. First of all, you're playing vanilla. I only play Conquests, so there are some things I don't know about vanilla. I'll do my best to point out when something has changed from vanilla to conquests, but I may miss a trick here and there.
Also, the analysis that I'm doing here is based on my playing style, which is moderately war-heavy. I've never had a culture win. I've never had a diplo win. My victories are mostly domination and conquest.
I see walls and spears all over the place. You're playing a defensive game. With cheap raxes and early archers, you could have been out kicking down doors a long time ago.
You're running 50% science, when more is possible. Are you familiar with the science and lux sliders? Hit F1 and look in the upper right. The sliders (look for the science beaker and the happy face) allow you to regulate science and luxury spending.
You're working towards a Monarchy. In Conquests, Republic is usually the government of choice, but Republic is stronger in Conquests than it is in Vanilla (IIUC), so this may be a good choice that you've made. I'll leave comments on vanilla governments to those who know more about them than I.
Why did you build the Oracle in Veii? You have all victory conditions enabled. I'm no good with culture victories (never had one), and the Oracle might be a good choice for a culture victory, it's no help for stomping your neighbors. It doubles the effect of temples. You have temples in many of your cities, far more than I would have built. Truth be told, I frequently go whole games without ever building a temple. The Oracle is 300 shields. That's a big investment at the point in time when the Oracle becomes available. If you haven't read Ision's "Four Rules of Wonder Addiction" in the War Academy, I'd suggest doing so.
You're in the ancient age, along with Egypt, Greece, and Babylon. Japan, China, India, and Zululand are all in the middle ages already. The Zulu have ~1400 gold. You have 198. Currency is known to 4 civs, but not you. Have you been trading techs? If not, you need to get more familiar with tech trading. The AI will trade freely amongst themselves and if you don't get in on the action, they'll outrun you everytime. Research from left to right in the tech tree. This will help you get monopolies on technologies, which trade better. For example, as Rome, you start with Alphabet (at least in Conquests you do). So one option for first research is Writing. Once you're the only one with Writing, trade it for The Wheel to Civ A, for Pottery to Civ B, for Masonry to Civ C. You can really speed up your research that way.
City spacing. Your city spacing isn't bad, but I see a little more CxxxxC than I would use. Part of that, however, is due to the terrain you were dealt and this wasn't an easy start. Where I see a problem is in your prioritization of tiles. To the SE of Rome, Lutetia, Antium and Veii are on the edge of a desert, while two cows with two BGs sit unused SW of your core. In the early game, food is king. That two-cow, two-BG area could have been a powerhouse, maybe a settler or worker factory.
I've got to tell you, though, that this was a tough start, from a terrain perspective. Your core is in the middle of tons of mountains that slowed your growth down. Mountains don't provide food, and the rough terrain slowed your workers down. You don't have iron and you don't have horses. That didn't help, either.
I also see that you've got 14 cities, 16 workers, and 2 slaves. That's not bad. Shoot for 1.5-2 workers per town. Gather as many slaves as you can lay hands on. They don't cost any upkeep (unlike workers that you build), so having a few hundred of them around by the time you get rails can be quite handy.
Suggestions for the next game: Do not build Ancient Age wonders. If the civ next to you builds the Pyramids, by all means, go take them. But don't build them yourself. Focus on settlers, workers and military. Unless you're going for a culture win, skip the temples and use the lux slider for happiness issues. And I'd say pick your victory condition early, as that will help you focus your city management. Knowing at 4000 BC that you're going for military conquest helps you decide whether to build a temple or another swordsman . . .
I hope this helps.
I haven't looked at the second game but I would like to add a couple of comments to what Aabra has said; particularly where he has said that he lacks knowledge of vanilla. I hope that they help.
