Don't be such a prude! Your moralism is out of place in a galaxy far, far away (and long ago)...

Yoda telling Luke that he didn't need weapons was strange, because JEDI use lightsabers all that time, and going into battle against the SITH without a weapon is stupid. I'm not sure what that was about... But, when I watch the fight scene, it looks like Luke is very angry, and probably filled with hate, because Vader "Killed" his Father, and he let those feelings control his actions, to win the fight... Yoda and Obi-Wan keep telling Luke that those things lead to the Dark Side, and that Luke should mind his feelings. Luke was also told he should be fighting with knowledge and skills, for Defense... Not Attack. When Vader's Mask showed Luke's face, I think that was to tell Luke that his actions were that of someone going to the Dark Side, and that he failed. Just like his father.

The fact that we know Leia is his sister makes this creepy and sick AF.

Great question. I bet he would have seen Leia in a sexy white frock with her hair down and a close-up of her pouty lips beckoning him to take her. Right?

What would he have seen if he didn't take his weapons?

I think Luke's failure is that he saw Vader in the first place, and then that he saw himself in the mask. Whatever he saw revealed the fear in his mind

His twin failures were reacting fearfully, and resorting to violence. VOTE FOR PRESIDENT ACKBAR 2016! " ...I assure you, my resolve has never been stronger!"

Luke's failure is that despite Yoda's insistence that "Your weapons. You will not need them.", he took them anyway, fulfilling Yoda's earlier statement (in response to Luke asking what was inside the cave) "Only what you take with you.". Some see the Vader in the cave revealed to be Luke as a hint of Luke's parentage, but I see it more as Luke's true enemy is himself (his anger and fear).

Yoda telling Luke that he didn't need weapons was strange, because JEDI use lightsabers all that time, and going into battle against the SITH without a weapon is stupid. I'm not sure what that was about... There was no Sith in the cave, or anything else he would need his weapons for. It was all in his imagination; a manifestation of his own fear.