Was there death of any kind before Adam’s great sin (i.e. the Fall)?
Many Christians, such as Ken Ham, would say no but other Christians disagree. For example, in the article linked to below, Matt Fradd explains how some Christians understand biblical passages such as Romans 5:12-14. The case that Fradd makes is essentially as follows.
First, the passage in Romans mentions death coming to all people because of Adam’s sin but it does not refer to plants or animals. Second, even in the Middle Ages (i.e. long before Darwin), theologians such as Thomas Aquinas thought that animals could have been carnivorous before the Fall. Fradd cites the following passage from Aquinas:
In the opinion of some, those animals which now are fierce and kill others, would, in that state, have been tame, not only in regard to man, but also in regard to other animals. But this is quite unreasonable. For the nature of animals was not changed by man’s sin, as if those whose nature now it is to devour the flesh of others, would then have lived on herbs, as the lion and falcon.
A third point on this issue is that since plants are alive, eating them would still have resulted in some type of death. One could also consider bacteria and other tiny insects that probably died as well.
Fradd’s full article on this issue is available here