Power steering equipped cars should have the final toe set with the engine running as it eliminates the play present in the box without the hydraulic pressure.
As far as the play,
1st verify that the box was centered in it's travel when the alignment was done. THIS IS CRITICAL WITH RESPECT to play. IF it was not centered you will have excess play
2. Verify it is actually in the box and not something else like a loose coupler or other component.
3. If it is in fact in the box that can easily be adjusted using the adjusting screw on top of the box. MAKE SURE THE BOX IS CENTERED Mark your starting location so you can return to it if needed. loosen the locknut and lower the screw 1/4 to 1/2 turn at a time. Recheck the play. If the box is not centered or you go too far the gears can be damaged.
4. The off center wheel can easily be corrected with minor adjustments to the tie rods. I have never allowed a car to leave my shop with an off center wheel. BUT do be aware that there is more of a "CROWN" on some roads that will cause an off center effect. So make sure the roads your using is not overly crowned.
4. Find a GOOD Frame and ALIGNMENT shop if possible as ALL of the above should have been done with the alignment. You may have to pay more than a tire store but I'm sure you know the cliché