Putting out Settlers is (almost) always good: in general, more cities = more everything! But yeah, that only happens if you
also develop the land around those cities! So for your next game, for every new 'core' town you found, you might want to try making your first builds a Warrior (to keep at least one citizen content) and then a Worker (to improve that town's tiles).
If the town is getting 2 food excess and 2 shields per turn, you can finish both builds within a single growth cycle, Pop1 to Pop2: the Worker-build will drop the town back to Pop1 with an empty food-box, but now you can build a better mil-unit over the next 10 turns (an Archer or
maybe Spear -- but see below), or start putting your first building into that town (e.g. if it's food-rich, build a Granary for fast regrowth, and use it to build more Settlers/Workers; if it's shield-rich, a Barracks for veteran units: if it's coastal, a Harbour for more food/ veteran boats; or if it's in your second-/third-ring, a Courthouse to reduce corruption for all subsequent builds, etc.)
This first is likely why you're getting bullied: If you'd had, say, 2-3 Archers/Horses per Spearman, rather than vice versa, the Inca would probably have feared you more, making them much less likely to try their extortion in the first place.
Depending on which direction you're working in, this
may be a little loose. Your towns can't get bigger than Pop6 without an Aqueduct (late Ancient), nor Pop12 before Hospitals (early Industrial), so packing your towns tighter in the early game might well allow you to make better use of more of the low-corruption tiles nearest your capital.
Say you found towns at C1-x-x-C2-(x)-x-C3: once you have Sanitation, you can build Hospitals in C1 (and later C3), while shrinking down C2 by building Worker/Settlers out of it -- which could then be added straight to C1 and C3 to get them quickly to Pop20, leaving you with C1-x-x-x-(x)-x-C3.Tut-tut.

Connecting (outer) cities back to the capital reduces their inherent corruption (and gives Happiness from any Luxes you've connected), making them more productive, earlier on. (Ideally, you should have a road all the way out to your next planned city-site,
before your next Settler is ready to roll.)
]And connecting the outer towns to each other allows you to shift your forces between (border)-towns much more easily in response to AI/Barb-incursions, allowing you to defend yourself using a smaller total pile of (fast) (attack) units. So building roads should be a high(est)-priority job!No, not really. Unless you're going for a Cultural victory, then you don't really need to build any of the Ancient Wonders, most of whose effects expire pretty early (Colossus and Pyramids
are really nice to have, though!). And at Monarch+, expansion and war in the early game can actually net you more of those Ancient Wonders than hand-building them yourself will do -- because by putting all those Wonder-shields into units instead, you can let the AI build the Wonders, and then steal them![
Once you've got a decent empire up and running in the Middle Age,
then it might be worth considering some some strategic Wonder-building, because once you've got the tech-lead, you'll almost always get any Wonders built before the AI can.
This actually makes things harder for you! For any given difficulty level, the territory gets filled up at a fairly constant rate (and remember, the AI always likes to found towns in a C-x-x-(x)-x-C pattern), but the smaller maps actually have fewer land-tiles per Civ than the larger maps, so they fill up that much quicker. And once there are no more 'good' city spots to be got peacefully, that's when the AI-Civs go on the warpath.
Also, number of each resource-tile initially spawned is directly related to the number of Civs placed at the start of a game (give or take a fudge-factor of plus/minus 1-2; this fudge-factor's effect is therefore disproportionately magnified, the smaller the starting number is), so smaller maps = fewer Civs = fewer resource-tiles = less likely that you will have any given resource handy to your starting position. And the AI-Civs also 'know' where all the resources are from the beginning, even before they've researched the tech needed to show them (to you). That's why they hustle to settle Tundra and Desert: it's for the Oil and Uranium they'll 'discover' there in about 4000 years' time!
MilTrad won't help you unless you have Saltpeter as well...