Accordingly, did Lord baelish know it was Arya?
He had never met Arya before, so he wouldn't know what she looks like. And he had no reason to remember her either.
Beside above, does tywin recognize Arya? Some fans have wondered if Tywin was ever suspicious of her true identity and realized she was a Stark, but this is unlikely. Petyr Baelish also visited Tywin during one Game Of Thrones season 2 episode, with Arya doing her best to disguise her face while serving him.
Likewise, people ask, why didnt littlefinger tell Tywin about Arya?
He did not reveal this info to Tywin because Littlefinger's business is knowledge, and how that knowledge can be useful. If he thought turning her over to Tywin was good for him he would have done so in a heartbeat. But he wanted more from the power this knowledge brought him.
Did littlefinger really love Sansa?
Yes, he does. He is not really in love with her, but he's is in love with her Tully part. Remember, the Hand's Tournament in the first book/season, he liked/loved Sansa's resemblance with her mother since then.