I'm sorry, but I can't resist. Despite that there are more experienced players out there who could address some of these points better. My knowledge is based on [GS].
"When you kill a barbarian scout, the barbarian camp that it spawned from will stop producing units for a while. So make sure to kill all of the scouts quickly so that you can take the barbarian camps out at your leisure."
I'm not saying this is wrong, but it's not how I interact with barbarians and scouts. When a barbarian scout finds a city and reports back to its outpost, that outpost will spawn about half-a-dozen units, and head towards that city. After that spawn, the outpost is quiescent a while. I think it eventually generates another scout, which has to re-find a city. But barbarian scouts prefer not to engage, so sometimes you can keep them from finding your city. Or if you know or suspect where the outpost is, you can keep the scout from reporting back. Either way, the outpost doesn't spawn that half-a-dozen. Outposts seem to defend themselves by slowly spawning units, if under attack, but maybe they are slowly spawning anyways, and I just happen to be attacking them. There can be advantages and disadvantages for removing barbarian outposts: they give you era score (for the first few eras) as well as gold, but if removed, somewhere another one will be generated (if possible), and it may not be where you like, whereas you know where this one is.
"Always attack with your ranged units first. This way your melee units take less damage when attacking, since they will be attacking a weaker opponent."
Not
always. If your melee unit wins, it moves into the tile of the defeated unit -- you may prefer otherwise. One common scenario for me is that I'm defending a city, e.g. against a barbarian horde like above. I have a melee unit inside the city, and range units behind it. I can attack with the melee unit short of it getting killed, then kill the opposing units with range units. Not only does the melee unit not become exposed, but it's in the best location for healing the fastest. The AI is not smart enough to employ this tactic.
"Ranged units deal more damage while standing on hills and shooting over rivers."
Nope. If you select your range unit, and hover over the opponent unit, you can see the factors that help or hinder each. Hills provide a defensive bonus, not an offensive one. And while melee combat suffers a penalty attacking across a river, there's no effect on range attacks.
"If you are competing with another civ for suzerian status of a city state, once you become Suzerian, declare war on the civ that is competing with you so that they lose all of their envoys with that city state. edit: this one no longer works. As a commenter below said, whoever you go to war with will regain their envoys once they make peace with the city state."
When you declare war on another Civ, your suzerain city-states do also. The other Civ does not lose any envoys, but their envoys don't provide their normal benefit. Well, if that Civ has Amani there, she is ejected, so I suppose that Civ loses those two envoys. But if, say, they had 1 less envoy than you, they could assign one more envoy to match, you'd lose suzerainty, and that city-state would no longer be at war with that Civ. If they assigned 2, they'd have 1 more, gain suzerainty, and that city-state would declare war on you.
However, if that Civ declares war on a city-state, they lose all the envoys they had there. Your being suzerain or not doesn't affect that.
One side-effect of a city-state declaring war on a Civ is that Civ loses its city-state quest.
I'll stop there.