Everything is simple enough. Some of your guesses are close to the truth.
MK One (1992):
Reptile is saying: "Look to la Luna!", "Blocking will get you nowhere", "Perfection is the key", "Fatality is the key".
That means you must be on "The Pit" location (there is the Moon in the sky),
and you must be lucky enough to see Santa Claus, a flying witch or a flying saucer (or Fergal's big face... or flying letters BYC) in the sky, or else Reptile won't challenge you,
and you must avoid touching the Block button ("blocking will get you nowhere"), except Sonya Blade's fatality (impossible without Block button, anyway),
but even if you fight as Sonya, never block the opponent's attacks before Shang Tsung shouts "Finish him/her!";
and if you fight as Scorpion, manage to do his fatality with no block button;
and you must do Double Flawless (perfection!) and fatality to your opponent.
[Sadly, rumors about the possibility of challenging Ermac, Smoke, Kitana, Mileena, Skarlet, Jade, Tanya, Nimbus Terrafaux, Lieutenant Pedro Sanchez, the ghost of Art Lean, Lizardlike Green Sonya (aka Aynos Crystal)... are nothing more than rumors.
Remember, the Warriors Shrine contains no Ermac! Ermac was just a programming glitch in MK One: there are no such secret opponent.]
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MK II (1993)
When Smoke the human (not yet robotized) linkuei warrior says "Mortal Kombat One", that means you will fight him in Goro's Lair (location from MK One).
When he says "You can START finding me", that means the START button is crucial to challenge him, when he's hiding.
When Jade says "Chun who?", she hints that kicks are crucial to challenge her when she's hiding. And Chun-Li (from Street Fighter) was always a master of kicks.
No, someone's guess was wrong, Jade and Chun-Li aren't the same person! Chun-Li is human, and Jade isn't (she is an Edenian immortal Yther woman, just like Sindel and Kitana).
The method of challenging Jade:
she's hidden behind the infamous "question mark" in the Battle Plan on the high mountain. When you fight the battle BEFORE the "question mark" (often it's Raiden, but not every time), you must avoid pressing punches, and High Kick, and Block, and Start. Use just D-Pad and Low Kick! Win the fight just with Low Kick (which means the footsweeps are allowed, and some specials containing Low Kick. -- e.g. Johnny's Shadow Kick, Liu's Bicycle Attack, etc, -- are allowed, too). If done correctly, Jade will invite you to "Goro's Lair" (on Sega Genesis/Megadrive 2, to "Blue Portal Zone", since the Sega console couldn't manage the Goro's Lair graphics, this time).
The method of challenging Smoke the human:
he's hidden in the "Living Forest". [Jade who is sometimes visible in the same forest is nothing but a graphical easter egg.] When you fight in the "Living Forest", do uppercuts frequently, Sooner or later, Ruthay the imp (played by Daniel Forden the composer/soundmaker) will show up in the right-low corner, and he will shout "TOASTYYY!", enjoying your uppercut. And then, while Ruthay is still visible, "catch Ruthay" by pressing Down+START. And then Ruthay will agree to arrange a fight with Smoke for you (he's a friend of Smoke). You will fight Smoke in "Goro's Lair" (on Sega Genesis/Megadrive 2, in "Blue Portal Zone", because "Goro's Lair" is unavailable on the Sega console).
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Sadly, rumors about the possibility of challenging Ermac, Kabal (supposedly in a cage), Skarlet, Ruby, Emerald, Orochi Hellbeast, Lieutenant Pedro Sanchez, Red Robin, Old Geezer Shang Tsung (from MK One), Hellspawn Scorpion (with no mask), Blaze, Hornbuckle, Kano, or Sonya... are nothing more than rumors. To highlight it, Jade says: "Ermac who?".
Hornbuckle and Blaze are fighting each other in the background at The Pit II, but that's nothing more than a background (in both senses of the word), duh, because Hornbuckle the Onaga's Cultists' High Priest tries to imprison Blaze to make him warm the dragon's egg to revive Onaga.
And Kano and Sonya can't be freed and/or challenged, though they are present in the background at the "Kahn's Arena".
And Shang Tsung can't do a Kano transformation in MK II, the line "Kano" in a sheet was just a prank from the developers.
You also can't make Hookality ("special pit fatality" with a hanging iron hook) in the "Dead Pool";
and you can't take a weapon in the "Armory";
and you can't feed your opponent to a treant.
Still, the Hookality (and a secret interaction with Kabal the time traveler... and a secret challenge to Ermac... and another one to Mileena...) will be present in Mortal Kombat: Shaolin Monks (2005).
The "Treant Eating the Opponent" trick will be present in the Mortal Kombat Shaolin Monks and in Mortal Kombat Komplete Edition 2011-2013.
And you really can pull out the supersecret "Fergality" in MK II , -- jump distance, Back, Back, Back, Block, - to transform your opponent to Fergal. But only playing as Raiden, and only in the "Armory", and only on Sega Genesis/Megadrive 2, and only if you did put the mark by the "Oooh, Nasty!!" section in the secret menu at the start screen. The mere fact of inputting of the secret Sega Genesis code destined to bring the secret menu (sadly I can't recall the code, google by yourselves) will bring the real Ruthay's face instead of "the face of Daniel Forden", i.e. Ruthay will shout "TOASTY!" with no "illusory disguise" on his ugly impish face.
