Yes.

ya its really easy

the one in earthrealm? before the white lotus society? i don't remember but i think there's a secret there. you can't get into the white lotus society area until you're done with konquest anyway. it's pretty easy to beat him. i think it may be a glitch in the game or something, but i've punched and kicked him and it still took away energy so you don't really gotta only use throws

lol i was playing him then i left the battle and it let me pass.... i then saw lui kang and i am now training with him

WHOA it says im fighting ghost but it looks like liu kang that u can see thru

Psst...you might want to start clicking "Add Spoiler" when you make a post like that. That's what it's for....
And yes, I did the defeat Jax with throws mission....it glitches though when I used Mileena against him. Throw him and then immediately use her teleport kick repeatedly and it'll register the damage from that even though it shouldn't.

I noticed this as well. However, some hits do not cause any damage at all. I did not investigate this further. However, my feeling is that it has to do with the attack meter above. I suspect that your attacks do damage if Jax's attack meter is in the red.
However, this is purely speculative.