Exactly what must be true in order for the relationship to be correct? and and and
There are some rules that apply when you're using "and." You must put a comma before and when it connects two independent clauses. (A clause is independent if it could stand on its own as a sentence, with its own subject and verb.)
But it's not always necessary to put a comma before and in sentences that join grammatically different types of words. Gita went to the shop and Rita played outside.
Likewise, it's not always necessary to put comma before and in a list. Many people have strong feelings about whether to use the Oxford comma in such lists, but there are no hard-and-fast rules for when you do or don't need it.