There is no reason you should have to. If the tie rod was knocked out of the spindle it goes back in the same place. Nothing else has any effect on the alignment.
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Depends on the car, not sure about your mits' - on mine all 4 wheels need to be aligned. If nothing suspenions wise is problematic then expect about 80-150 bucks. if you go to pep boys it is 69.99 for a four whell alignment
under the car about two feet from the front of the car
A two wheel alignment or a four wheel alignment? Where are you located? I'm near philly two wheels start at around 50 bucks four wheels are closer to 100. Best bet is to call up local shops near you tell them what you need and see how much they charge. Each place is different and it also depends on which you want obviously.
Assuming that the wheel does not have a stuck brake then the wheel bearing is froze. The wheel might break free by rocking the trailer front and back but probably the wheel will have to be removed and the bearing will need to be replaced.
Although there is a snap ring retaining the bearing, you will need to take the strut to a mechanic and have the bearing pressed out. If you take out the three bolts on the top of the strut tower, and disconnect the ball joint at the bottom, you won't have to worry about throwing the alignment out.