Monarchy sucks for tech. I usually play huge maps, and on regent the easiest way for me to get ahead is to quickly expand, foregoing infrastructure. I send out a settler, have it build its own spearman, and by then it is usually ready to build a settler. If the settler will be done before the city reaches size 3, I will build either a temple, or library, depending on which is cheaper.. The civ you choose has alot to do with what you should do with your workers. If you are industrious, you can get away with fewer workers because they are twice as fast. I have enough workers that all of my cities are connected by roads within turns of their being founded, if the workers haven't gotten to the site before the settlers. Every road square that your population is working on gives you commerce, which means more science, add the bonus for republic, and you should be able to stay even. I usually play on pangeas, and go for the Great Library first, if I have 2 cities with a high production, I will go for the Pyramids too. To me, they aren't as important, but that is probably because I have always played any game with techs with the same strategy, I win through superior technology. Once my core cities get too far away from the borders, then I start building temples and libraries. Usually, through the first age I am a bit behind in tech, but the GL keeps me right behind the other civs. I keep my science set high, to make sure that I get republic as soon as possible, then go for the military tradition line. That way, when education is discovered, I will get it with the GL, and be a tech or 3 ahead in the other line. Depending on the situation, the other civs might be able to stay with you in tech until you get railroads. This is where the number of workers you have can make a huge difference. The shield bonus they give you will mean that no one will be able to challenge you for tech or production leads for the rest of the game.
As for your war problems, I have 2 suggestions. First, I trade my world map every 10 turns. you can do it more often, I just like the year breakdown, especially in the AD years. 50 AD, 150 AD, until it switches to 5 year turns, 1600 AD, 1650AD, until it switches to 2 year turns at 1750, ect, just an easy way for me to check how long it has been. The more you trade with someone, the better your relationships are. For the second suggestion, it sounds like you need more allies. Since most of my cities are defended by 1 defensive unit, best I have at the time (this is where spearmen are better than warriors, they upgrade all the way to mech infantry), I get 3 other civs to declare war on anyone that declares war on me. 2 civs on the borders of the one that declared war on me, to distract their forces, and 1 between us. If there isn't one between us, I pick somone on the other side of me, they will send their forces through my territory, and meet the aggressor head on if he managed to spare any forces to attack me with because of his other 2 front war.
With this strategy I am never that far behind in tech, I get most if not all the middle age wonders (especially with prebuilding a palace), and get to attack riflemen (at best) with tanks.
Other people have a completely different strategy, they find this one too boring, they find an early military approach works better for them. I have had some success with this too, but I prefer the peaceful scientific style better, you just have to learn the keys to doing it successfully, maximizing your commerce. Roads for the bonus, temples and cathedrals to keep your people happy and working, libraries for science boost, and market places for their bonuses to commerce. As for building wealth, usually I am getting techs fast enough I always have something to build until the fourth age, occassionally I will switch a city to wealth then, depending on the size of my tank/mech infantry forces.
"Workers are the most powerful unit in the game" (except for settlers). You need workers laying down roads, so your settlers don't take so long to get where they are going, roads for increased commerce (and science), mining for more shields, irrigating those plains, etc. I like to have at least 1 worker/city. I will stay with 1 worker for my first 2-3 cities, but then I set aside 1 city to pump out almost nothing but workers. You can also buy workers from the AI if you want to check with them every turn to see if they have any for sale. They usually cost anywhere from 25-30 gp (price varies on things like reputation, attitude, culture, etc.), but they cost no upkeep, so even though they are slower, they don't cost you anything for the rest of the game.
