What basic ethical principle assumes that individuals have the right to live their lives as long as their actions do not interfere with the welfare of others?

The correct answer should be the ethical principle of autonomy.
It means that you can do whatever you want, as long as you're not hurting anyone else, and as long as it is legal. Once it stops being unharmful to others, you lose the right to do that. It is an important principle to abide by, especially in medicine.