If you are seeing wheel wobble like an old bicycle, then you are describing the wheels being out of true.
I agree. It sounds like it needs to be re-balanced and trued. I don't know how to true wheels. As for balancing, I would take it back to the place that installed the tires and ask them to balance it again. They shouldn't charge you anything for it, since they messed it up to begin with. They can probably true the wheel too.
To test the forks, just hold the brake and push them up and down. Unless they stick somewhere in their travel or you see some oil leaking from somewhere, they are probably fine. These are simple forks and likely will never need to be replaced.
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