No, they don't. They don't have to be "life" as we'd recognise it. They just have to be biological entities that can reproduce. Small, simple things that can make more of themselves and change.
The difference between "life" and "not life" isn't sharp. There's no clear gap between the two. Rather, there's a number of gradients of complexity and structure that humans put an arbitrary line (or series of lines) across.
Sure I can.
Bacteria fit pretty much any definition of "life", they're probably the most common form of life, but they're neither animals or plants. They're not even in the same domain as animals and plants, as their cells don't have the same structure.
Viruses probably aren't life - they fit some definitions but not others. But they're probably the most common type of reproducing biological entities. They're still out there, in their quadrillions, reproducing, but they're not animals or plants either.
Prions definitely aren't life - they're basically complex proteins. But we know that they can reproduce and evolve via mutation (
even though they lack DNA), suggesting that even without DNA/RNA, relatively simple combinations of chemical interactions can become progressively complex.