In Return of the Jedi, When Luke asks Leia if she knew her mother, Leia seems to think for a moment, almost as if drawing from the Force.Yoda wrote:Concentrate...feel the Force flow. Yes. Good. Calm, yes. Through the Force, things you will see. Other places. The future...the past. Old friends long gone.
As for the Lightsaber, I think that this can be explained with the statement on point-of-view. I do believe that Anakin Skywalker would want for his lightsaber to be passed down to his offspring. Whether said aloud or not, I do believe that with the way he used to show-boat, he'd want to show his kid(s) everything he knew, which would include any lightsaber tricks, and giving the lightsaber would probably be included.
And finally, the name. As we never see him say his name to Owen or Beru Lars, I think we can write that off to a few things. 1) he was trying to hide, and also commune with the Force (and Qui-Gon) at the end of Revenge of the Sith. 2) as he was hiding out, word of him there may have reached the local villages/inhabitants, and his name somehow "leaked". however, this could be construed as a case of that "telephone" game you play in school (where a phrase is started at one end, then told person-to-person until the end with no repeating, then see how accurate it is at the end). Te name just ot changed over time, and as he was trying to hide, Obi-wan never bothered to correct them.
I know I could be stretching things a bit, but I feel these are kind of easily explained. Now, I'd like to know how Obi-Wan goes from looking 30 to looking 60 in the span of about 16-18 years. Also, how is it that Technology (and species) takes a nose-dive and things go from big to tiny in the course of that same 16-18 years.