Batter walks and overruns 1st base

[Hi Neighbor]

There are two situations that I would like to hear your thoughts on. Lately, both seem to be interpretted calls. Please let me know if I have missed a rule.

The batter walks and overruns first base

1. The catcher throws to 1st base. 1B tags the batter-runner who jogged up the line after touching 1B

2. The catcher returns the ball to the pitcher before the batter-runner touches 1st base. The Batter runner overruns the base, (making a sharp left turn), and then immediately returns to 1st base. She made no effort or feint to go to 2B.

My interpretation:
Out on 1. She forfeits her exemption after touching 1B on a walk.
Safe on 2. No effort, no feint, no stop

Thank you