Here are the corrections:
1. Rita likes to draw, to write, and swimming.
Corrected: Rita likes to draw, write, and swim.
2. Acting is better than to dancing.
Corrected: Acting is better than dancing.
3. Ellen spends her time reading, listening to music, and she works at the mall.
Corrected: Ellen spends her time reading, listening to music, and working at the mall.
4. Jan appeared on a talk show, visited with Vanna White, and a meeting with Tom Cruise was arranged.
Corrected: Jan appeared on a talk show, visited with Vanna White, and met with Tom Cruise.
5.