Yes but generally speaking Katakana is used for writing foreign words. Hiragana is used in schools as the basis for teaching Kanji. An adult will use a mixture of all three in everyday life.

It's very possible but not very common. To an adult Japanese person it would look a bit strange and might be more difficult to read. When computers first came to Japan they didn't have enough memory to store kanji so word processing was all done in kana. If you download an emulator for the Nintendo Entertainment System and try to play a Japanese game, you'll find that very few kanji were used, even for games with a lot of text like Dragon Quest. Since Japanese doesn't use word breaks, the writers would adopt some adhoc system to make the text more readable. As another example, I think one of the first Japanese versions of the Bible was written entirely in Katakana.