There is a massive gap (IMO) between warlord and prince

I produced an archer and my gold went down from 4 to 3 when he was produced.

I kept him in the city but the gold stayed at 3, why is this? I had 2 others units (a scout and warrior) exploring at the time but gold only went down from 4 to 3 when the archer was produced.

You pay maintenance on every unit -- military, worker, settler (until you settle), great person, missionary, etc. In early eras the cost is 1 gold per turn, and it rises in later eras.

If you adopt Tradition's Oligarchy policy, any garrisoned unit will be maintenance free. If you haven't adopted Oligarchy, garrisoned units aren't free. If you are playing vanilla, you have to click the magic garrison button to get garrisoning benefits; in G&K, it is sufficient for the unit to be in the city. If you were to delete your wandering scout and warrior, I suspect you would see your gold per turn rise by 2.

Later, Freedom's Free Speech policy gives you 8 units maintenance free, without any garissoning requirement.

Wonders can be a part of victory at any level (even immortal & deity) but you do need to be more careful about when and which one to build as difficulty increases, and prioritize conquering them rather than building

I agree with OP about the jump. When I first bought the game, Fall 2010, I could beat the first three difficulties on the first attempts at each - but Prince took a while to get a win, and it took about a year before I was winning every game I played. (King took only 3 months for me to "master", and I win most of my games in Emperor now.)

These are the tips I would give you:
- Don't neglect your military (which doesn't seem to be your problem)
- Don't OVERemphasize your military (it's expensive, and you don't need the biggest, you just need to discourage them from attacking)
- IF early war are still a problem, settle your cities on hills, or use mountain ranges and other natural features to make it harder for them to attack you
- Try to avoid war with AI (this seems to be a problem for you)
---- Don't expand towards the AI civs, especially if they are expanding towards you
---- Make some early trades to gain favor with them
---- Make 1-2 Declarations of Friendship to help stave off war
- Reseach the tech that get you Composite Bowmen if you are having too many war problems
- Make sure your cities are growing - more population = more science
- Sell luxuries for cash when you don't need the happiness early, buy settlers, or keep cash on hand for emergency military buys


The biggest thing though is to make friends with the AI. I'm not sure why you are getting into so many wars that you've had to militarize so much. I play on Emperor and I find it relatively easy to stay war free as long as I don't expand too quickly.