1. Confier est un verbe, it means to tell someone a secret, or to charge him to carry about something who counts to you " je te confie la garde de mes enfants " " je te confie les clés de ma maison " means " I entrust my kids/home to you ".
2. Confiance est un nom, it means The Trust > " Je te fais confiance " = " I trust you "
3. Confidant is the person whom you tell you secret, the person whom you tell everything and you are very close to him.
4. Complicité est un nom, it's when you are very close to a friend and that you have a lot of fun together, you can share a lot with him, in French we could say " J'ai beaucoup de complicité avec ma soeur " In English I guess the word is " in collusion with ".
It can also mean that you've seen or helped someone doing something wrong and you didn't tell, for an exemple " Avec la complicité d'un de ses ami, le tueur a tué sa petite amie" > " With the complicity of his friend, the killer killed his girlfriend".