I think he probably did; he mentions her in his dying moments and asks Luke to tell her that he became good again which suggests that, even though he never interacted with her knowing he was her father, he wants her to know that he was able to do good.
As to the second question, it's mentioned in the third film that Qui-Gon had learnt to come back and it's implied that he taught Obi-Wan and Yoda (not sure how Anakin managed, possibly on his own like Qui-Gon did or maybe he was taught as well, it's never said) to do the same. I don't think people who aren't Jedi or Sith can come back in that way, which is why Padme and a lot of others didn't come back.
Of course he loved Leia (l checked wookiepedia)
Padme didn't appeare as a ghost 'cause..well, first resson is
-She's not a jedi
-And only Jedis or Siths who learned how to appeare as a ghosts (like in Revenge of the Sith at the end when Yoda asked Obi-Wan to go to Tatooine, there he will learn about spirit's world by Qui-Gon Jinn)