Why В мене є instead of У мене є?
"У" and "в" mean the same in this case, but at the beginning of a sentence before a consonant you should use "у".
How do you know when to use either сім'я or родина for family? As fas as I know they mean the same thing.
"Сім'я" and "родина" are synonyms. You should report it, if one of them is not accepted.