I am wondering if my tie rods need replacing or if the problem was just that my tire was unbalanced.

I noticed a rhythmic clicking noise, which a couple of days later was found to be associated with my steering wheel shaking a bit as well, in sync with the clicking noise.

I rotated the tires and the clicking noise and the steering wheel shaking is gone. I also noticed that one of the tires is worn on the inside (driver side). I also noticed that the passenger front wheel can be moved a little bit with my hands, and I also noticed this loose piece. I have attached videos of these things. I will get an alignment, but do I need to replace the tie rods? If so, do I just replace all four or just the one in the video? That is the outer tie rod, right? Video links below. Thank you!

Wheel

Tie Rod?

 

If you're going to replace any tie-rods, do that before the alignment.

 

Your links didn't work for me unfortunately, but if you can wiggle the wheel left/right by hand then you should replace all the inner/outer tie rods. Also, the clicking noise is usually indicative of bad cv joints so inspect those as well. Replace the tie rods before you get an alignment and while you're at it, I'd also replace the upper/lower ball joints as well just to freshen things up. If they're worn like your tie rods then you'll notice a big difference in driving after you get your alignment.

 

Could you try to see if the links work now, please?

I had both axles replaced recently because of a clicking noise with turning, but this clicking noise resolved after I rotated the tires.

 

Your tie rods bushings are shot. From your description, it's also possible you have a bad axle or wheel bearing. I agree this should be fixed before any alignment.

 

Does a wheel bearing require alignment after? Was thinking about getting tie rods and bushings replaced then get an alignment, and maybe wheel bearing later if needed

 

A worn out tire from camber wear or a flat spot on the tire can cause shaking.

 

Wheel bearing No, tie rods Yes.