"We are the children."
Yes, אנו is correct, but it's usually very formal and only used in formal or official letters/correspondences.
sophit means "ending" to mean ending nun, so you will find and use it only at the end of words
Because neither word ends with a nun. Nun sophit is only used at the end of a word
I know ילדים means "children", הילדים means "the children" and וילדים means "and children, but I was given the choice to select בילדים and לילדים too. Are they real words? If so, what do they mean?
the ב at the beginning of a word means "in" or "on" so you wouldn't really use it much for children, maybe if you wanted to say "I put shirts on the children" when saying a noun is definite (ה) with the ב you pronounce "bah" instead of "b". ל is used to mean "to" so your example would mean to the children. Same principle of combing the definite "lah" versus "l"