The two sentences are rather similar. Usually we might say "We are family" about another person. It means that we are either related or that we are part of a close group. "we are a family" would be used about a group of people who are related or part of a close group. I guess there is some flexibility but that is how I would use it.

“We are family” would usually mean “we are in the same extended family”. You might use it if you wanted to explain to someone else why you were acting a certain way with other people. You guys make so much noise together. Yeah, we’re family. (They are my cousins, aunts and uncles, nieces and nephews etc) Why does Uncle John invite us to Thanksgiving every year even though he and Dad always start arguing? We’re family. He has to invite us. “We’re a family” is what you might say to someone in your own immediate family, to remind them of their obligations. But, Mom, I hate going to the fireworks every year. Understood, but we’re a family and we’re doing this together.

Both seem ok to me. "We are a family" is gramatically correct. "We are family" is a little less formal - but both can be used.

We are in a family is good, we are a family is understandable but the actual English is a bit off when you think about it. We are family is song title.