I just had my right outer tire rod changed, do I need to get a front end alignment?

Yes, if it was not done when the tie rod was changed. In the old days I set toe by putting duct tape across the front tires and centering the wear, adjusting toe to wear slightly outboard for stability. Modern cars need more precise alignment than that.

Absolutely because even though the outer tie-rod *end is screwed on the tie rod the same number of threads there is no guarantee the body geometry of the new tie-rod end is the same size as the old one. The exact toe-in angle will have changed.

Yes, the alignment needs to be checked.

That's the thing about alignments, unless something is really wrong, you never know if you "need" one or not. In this case it would be a good idea though.

Who ever installed the tie rod should have done it. If they did not then you should have it done.

If the shop mechanic did it he would have counted how many rotations it was in so he could repeat it with the new tie rod..so nothing would have changed. If, when you drive down the road and you can let go of the steering wheel for 3 seconds and the car does not wanter off the road; then you are probably good.

You at least need to have the toe-in checked. That would be the only thing that would be effected by changing the tie rod end, but most shops want to only do full alignments.

yes

Yes

Yes.