No, and no. Lifegain cannot be redirected to planeswalkers, and you cannot choose to redirect damage to your own planeswalkers, because there are no rules that allow you to do either of those things.
As you surmised, planeswalkers don't have life in the first place, so it would make no sense for them to gain it. There is a rule involving planeswalkers and redirecting damage, but it only allows you to redirect damage your sources would deal from
your opponents to one of
their planeswalkers. (And your opponent can do the same to you, if they so choose.) What that boils down to is basically, "You can use
Lightning Bolt to deal damage to your opponent's planeswalker“, and ”You can choose to have your
Earthquake deal damage to your opponent's planeswalker rather than them, but you can't choose to throw one of your own planeswalkers under the bus to save yourself."
If I can make a helpful suggestion, this forum probably isn't the place best suited for asking most rules questions–its focus is providing definitive answers in situations where other reliable sources disagree on the correct answer or where the associated rules are themselves unclear or incomplete. For straightforward questions about how things work, there's a wide variety of other sources to choose from, including the
#mtgrules chat room,
Cranial Insertion, the
Ask A Magic Judge Tumblr, or even the dedicated Rules areas on the larger Magic forum sites, many of which will provide answers that are just as correct and informative, and often far faster than you'll receive them here. There's very few people able to post answers here, while more open venues often have multiple people available specifically to answer whatever questions might happen to be asked at all hours of the day.