Runner on 3rd; Batter walks, continues to second?

[yscleo]

There's a runner at 3rd, with 1B and 2B empty. Batter/runner gets a walk and runs toward 1B, and turns to go toward 2B.

Does the batter/runner has to touch the white part of the first base bag in order to run toward second, or either part of the safety first base bag is good?

Does the first base fielder has to be out of the way, or can s/he be just by 1B ready to catch a throw from the pitcher?

Thanks.