Riven really doesn't get crazy amounts of kills unless the enemy is stupid, pre-3 she doesn't have a full combo, at 3 she can do a good chunk of damage if you land an auto between each ability + ignite/exhaust. She starts to get her kills once she gets a decent build, frozen mallet, maw, wriggles, maybe bloodthirster, things like that that make her tanky so she can continue to chase with her abilities, if you just outlane the enemy and harrass enough that they recall and miss on farm, you'll dominate him anytime your ult is up, and eventually you may be able to 2v1.
Personally, I start with my stun at lv 1 incase of any early game fights that I don't want, shield at lv 2, lets me dash in and use my stun to safely get last hits, q at lv 3, and thats when you harrass the most. E in, auto, stun, auto, q auto q auto q auto. Or at least do as much as you can before the trade stops, once you hit 6, harrass them down a bit, do a full combo with your ult activated, use your ult as a finisher, easy kills
Most champs don't 'fall off' late game as much as the other team builds against you and you don't counter it back. Lux is a champ that wrecks, but once they get magic resist you just don't do much. I played against a morde once, wrecked him all game until he bought enough magic resist that I couldn't scratch him anymore until I got a void staff, and it was too late by then.
Most of the champs you listed don't fall off either, graves and darius wreck, morgana's ulti wins teamfights, lee sin wrecks, fizz and wukong are great as well.
Any ranged ad carries have their prime game late game, with a full build, and as long as they stay alive they'll melt the enemy team. Caitlyn is sort of an exception, as she's got the range and power to let her have a good early game, but no steroids and little utility to keep her as strong as someone like vayne or trist late game with a full build.
Shyvana is a champ that does a lot of damage any time of the game, fast jungler, strong top, the downside is no cc or built in sustain. You have to play it safe until you get some resistances or life steal to keep you alive. She doesn't really get shut down late game because she has a built in armor shred (her fireball)
Dr. Mundo builds warmogs and goes where he pleases, throwing cleavers that (at lv 5) do a HUGE % of enemy's current health, aoe w, built in ad steroid on his e, ult is short cd that nearly fully heals him. His counters are basically ignite/executioners calling (QSS/cleanse?) and madreds bloodrazor (which you build a force of nature against) Depending on what level you are, a good build to aim for would be 3 warmogs, atma's, force of nature, merc treads. 6k hp, something like 300hp/5 seconds, autos for ~300 with his e + an built in sunfire cape that you can have up forever once you get enough hp regen.
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