Will lady tsunade from naruto Shippuden come back alive after the fight with pain?

Answer 1

Lady Tsunade was unconscious, not dead. It has not been released yet in the Naruto Shippuden episodes.

Note: Though, I read through some manga's and I found out that Lady Tsunade has finally awaken from conscious.

As well as Lady Tsunade was not fighting pain, she was protecting everyone in the Leaf Village from Pain's jutsu that crushed everyone in the Leaf. Lady Tsunade had to use all of her power to save as many people as she can from the explosion, which caused completely all of her chakra.