I think that Frodo's compassion is inherent in his character and that this, combined with his memory of Gandalf's words about pity for Gollum are a large part of the reason for his treatment of him. There's also the fact that Gollum at one point swears 'by the precious' to help the Hobbits, and Frodo believes, at least up to a point that this oath will hold good for a while, as indeed it seems to do, as in the time when both Hobbits go to sleep, and Gollum has his 'slinker and stinker' debate.
As to Gollum's redemption, I would say that if, indeed he was redeemed, then it was not a concious action that caused it. Gollum had no intention of destroying the Ring, or himself for that matter, and whilst, in fact he did both, thus in effect saving both Frodo and Sam at the expense of his own life, the involuntary nature of the act implies to me that he had no intention of trying to 'be a better person', and was acting from purely selfish motives, hardly a recommendation for redemption, I would have thought.
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