When you've just seen a spider in your room, it's better to ask, "What is this?" This is because the spider is right in front of you, and "What is this?" is a more natural and immediate way to inquire about its identity. Regarding the second question, both "A spider ate another spider" and "One spider ate another spider" are correct ways to convey the idea that one spider consumed another. The choice between them depends on the context and the level of detail you want to provide. "A spider ate another spider" is more straightforward and general, while "One spider ate another spider" is slightly more specific, emphasizing the individual spiders involved.

It depends where you are and what you know about spiders. What’s this? will often require an answer more detailed than ‘A spider’ because we know what a spider looks like. ‘What is it?’ can also work depending on how you identify what you’re looking at. For example I see something moving on the wall over there. What is it? I’ll go check. It’s a spider. (Pointing to something far away that I know you’ll see) What’s that? (After walking over) It’s just a spider. (Pointing to something close, obviously a spider but I don’t know what kind.) What’s this? (Looking closely) That’s a wolf spider. They’re common but they don’t usually come indoors.

As you point at the spider, say “what’s that?” if it’s at some distance. If it is very close, say “what’s this?”