Is it possible to save Shawn at all?
I tried picking up the plank to hit the zombie, tried punching the same zombie, tried pushing the tractor off Shawn, all to no avail. Is it because I am not fast enough?
No, there's no way to save Shawn. Regardless of what you do, the outcome is always the same.
Depending on your choices, and how you respond to Hershel afterwards, you can change your relationship with Kenny, but he'll always offer you a ride to Macon regardless.
Both major events (Shawn's death, and Kenny's offer) are scripted and key to the plot, so there's no changing them.