When I'm driving at around 110-120kph, the steering wheel shakes. Is this a problem with the alignment?
Speaking of alignment, the car pulls to the right when I'm not holding the steering wheel. Should I go and get my wheels aligned?
I fail to see how. It may cause the tires to follow the road, which in turn moves the steering wheel, but it wouldn't cause anything I'd describe as 'shaking' or vibration that comes from an off balance (or even out of round) wheel.
You basically argued against yourself. The tie rod end is the problem in that scenario, not the alignment.