1)Should the broken remote be removed? Yes.
2)Should Cursed Eye be removed? Yes. The way I see it, with two racers with comparable skill level, the only major difference comes from how many uses it takes to get a good teleport, which is a terrible concept due to the teleports using a limited resource (health). I agree that it takes skill to use, but so do such a number of items used in speedrunning and racing that it's not much of an argument in my eyes.
3)Should telepills be removed? No. Pills are even riskier in seeded than unseeded. I don't think removing telepills would have a positive effect on the format.
4)Should the shop pool be modified to make it better? I personally don't care, but if forced to choose I'd rather keep it in its current state.