He doesn't fully trust her, due to her history as one of their past opponents.
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Robin has more gadgets and he learned jujitsu from Batman eventually taking his place, so I'll go with him.
This question isn't categorized so I don't know exactly what your talking about, but if you mean Zoro from One Piece the thing around his head is his bandana. The same bandana is usually tied around his left bicep but he ties it around his head when facing difficult opponents. If you meant the other Spanish Zoro with a mask then I have absolutely no idea.
Eiichiro Oda, the creator of One Piece, has specifically said that there will be no romance in One Piece and so there will be no couples. Therefore, Zoro and Robin will never "get together". If you've noticed, no crew member actually expresses any romantic feelings towards each other, except for Sanji, who acts on lust alone and will do so for any pretty face regardless of personality.
as a friend yes, but as a girlfriend no. he dosent value women like that. if she attacked him and they werent friends. he would attempt to beat her up. that goes foe any other female foe
Zoro follows his own code of honor. While the majority of the actions that he does have good consequences he is prone to bursts of violence.