Will the new lower balljoints and tie-rod end rust if I keep them natural metal? Should I paint these if I want to avoid rust on these new parts?

yes they will rust. yes if you are anal like me you should paint them. I use castcoat engine enamel after a couple coats of primer then I get jamming clear and put a couple heavy layers of clear on them.

The cast coat is high temp and is more durable if you cure it with heat. I have tried a variety of methods and prefer my heat gun.
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Honda cb1000
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ZX14 VS HAYABUSA

I've never had a car with new balljoints and stuff.
I'm anal, but maybe not as much as you.