Thanks a lot for your time to look everything over and detailed suggestions. I agree that my city management needs improvement and I've been reading articles on the site to get better.
That's the way to go.
I did get liberalism in a previous monarch game with Alexander (that also ended poorly) so I'll try to go for that more consistently in the future. The thing is that in this game, I didn't have sailing and compass researched yet, and I didn't want to take the time to get them so that my GS's could lightbulb more advanced techs but I'll do that next time.
You can lightbulb Paper even if you don't have Sailing yet. The lightbulbing order isn't the order in which the techs are available. For detailed lists for each Great Person take a look here:
Great Person Tech Preferences. Thus, unless you research up to Optics, you're pretty safe in trying to get Philosophy, Paper and then Education through lightbulbs. Even if you do get to Optics and a GS lightbulbs it instead of Paper just research Paper on your own, then lightbulb Education. Paper is pretty cheap anyway.
I was trying to get a great artist for some cultural support in newly conquered territory...but it won't be any use this time.
I've had the occasional Great Artist settled in a conquered city, or build a Great Artwork in it, but it's really situational. I'd rather have GSs.
I play on monarch because I am trying to throw myself in the deep end. I think doing it that way will make me climb the learning curve quicker by paying more for my mistakes. And even with aggressive AI, nobody has attacked me in this game and Mao even gave me Feudalism for free. Not very aggressive...
Receiving techs for free isn't a good sign. It usually means you're so far behind the others don't see you as a threat. I wouldn't play Aggressive AI anyway at first. That's usually like a Monarch+ level. Pretty tough if you ask me.
By the time I had an army of swordsmen to take down Egypt (which I would have done had they not become Mao's vassal), the Chinese were already just too strong so I held them back, hoping to get to chemistry and attack.
Wasn't there anyone else you could attack early? Egypt with the War Chariots and the protective Chinese aren't the best targets. If I can I usually attack with Axemen in the first war. But in this case they might not have been enough had you attacked one of those two AIs.
Sometimes I can grab a few wonders in the early game if I have resources, but often the AI just races ahead and I never catch up.
On Monarch I choose my wonders very carefully. Often going for Pyramids or some big wonder is too high a risk to even consider. The Great Wall is a pretty good one, especially combined with defensive starts to your wars; with some luck it might get you a GE for free Pyramids! The Great Library on the other hand is usually easy to get and it's especially useful for a Philosophical leader. But everything depends on the situation at hand. Take a look at aelf's EMCs and IMCs and Sisiutil's All Leaders Challenges to see how different wonders work with different leaders.
Do I just need to manage cities better, choose my techs more wisely, use GPs better and strike sooner? Thanks again for all the help.
Yes, yes, yes and yes.

There are some pretty important techs out there that you want to take full advantage off. Things vary of course with your leader's traits (ex: Code of Laws becomes more important when you're Organized and have cheap courthouses), but here are a few that are most useful:
- Alphabet: early tech trading can make you friends; usually you can also trade it for Maths and/or Iron
- Literature, especially if you're Philosophical (or Industrious) for the Great Library
- Currency & Code of Laws for extra trade route and courthouses: means you can expand your empire to more than 4-5 cities without driving your economy into the ground
- Civil Service - Bureaucracy gives your capital a huge boost: 50% more hammers and 50% more commerce!
- Liberalism - gets you a free tech and some pretty good civics (especially Free Religion if you can't afford to adopt a state religion)
Being Spiritual also opens up other paths. For example you can get and spread an early religion and get a shrine for it to fund your expansion. Or build the Oracle to get Code of Laws very early.
You can even get down a level to try different approaches, it's nothing to be ashamed of! Then, once you have a few things worked out, go back to Monarch and you'll have more fun and learn more if you do it this way. Struggling game after game isn't that much fun...