(1) Do you want to pee/poop --> perfect! "Would you like" seems a little too polite to use for a child, although it is not wrong.
(2) Good! You can also say "give me the phone on the table."
(3) I wouldn't call a baby "baby" to his/her face. You can refer to a baby as a baby in the third person (e.g., "that baby is soooo cute!"), but when an adult calls another person a "baby," I usually think of that person as the speaker's lover. Instead, you might use another term of endearment, like "come on along, pumpkin!" This is just my personal habit, so others may have different opinions on this...