1. Testing reality is important because it's very easy to believe everything we see or hear without really knowing if we're dealing with facts, suppositions, or feelings.
2. Descartes also said, "I doubt, therefore I think, therefore I am." Tweedledee and Tweedledum made Alice doubt she was real, which made her question her own reality. Alice said if she wasn't real, she wouldn't be able to cry. In my opinion, her argument is valid because tears are an expression of one's feelings. If she wasn't real, she wouldn't have feelings.
3. According to Descartes and theoretical scientists, consciousness of self is an important test of one's reality. Logically, if you don't exist, you can't be aware of yourself.
4. I don't know how to answer this question.