Greetings @MoveMountains, great questions.
There are different responses to this questions by Christians. My take is that I don’t necessarily see anything in the Bible that prohibits the receiving or donating of organs and I am persuaded that organ donation could be an amazing expression of love and compassion. It is also important to understand the intricate details/discussions surrounding organ donation e.g when is someone considered dead medically, as this can have a profound impact on how one answers this question.
Here is an article that explores the various questions and responses/arguments that can be made on this topic: