Can the organisms of any trophic level be removed without causing any damage to the ecosystem? Will the impact of removing all the organisms in a trophic level be different for different trophic levels?

No, the organisms of any trophic level can be removed without causing damage to the ecosystem. By doing this there would be an imbalance in the ecosystem. Yes, the impact of removing all the organisms in a trophic level will be different for different trophic levels. If the producers are removed then organism belonging to the higher trophic levels will not be able to exist, as produces form the basis of the food chain being in the first tropic level. Similarly, if the organisms from other levels are removed then it will affect the next level causing the extinction of organism of that upcoming level.