Not exactly. She did go blind as part of her training with the Faceless Men, but she woke up blind a little after killing a man of the Night's Watch that had deserted them and came to Braavos. She chose to continue with the blindness. The Kindly Man, the Faceless Man at the House of Black and White, would frequently ask if she would like her sight back, but she knew that if she said 'yes' they'd kick her out. Jaqen H'ghar is not involved at all with Arya's training. She never sees him again after he gives her the coin and leaves Harrenhal. On the show, when Jaqen changed his face before leaving Arya, he kept that face and when to Oldtown calling himself the Alchemist. He then kills a student of the Citadel named Pate, takes his face and is now in the Citadel for some reason that hasn't been revealed.
when I rewatch their beef pre-littlefinger execution, as the two weirdos might have played some sexual tension in there.
