The food from the waste products of animal agriculture will get more expensive, as animal agriculture shrinks in size. The price for all "traditional" slaughter meat will go up, as it loses the economies of scale.

>Will we still grow animals?

We still raise horses, but far fewer of them than in 1900. Look at whatever dish you have in mind, and ask if you would pay enough for that dish to raise the whole animal. These niche products will have to carry ever more of the cost of raising the animal.

>Will we have other sources to get flavor for broths?

Cultured fat is a thing, too.

>How will I be able to get teriyaki chicken hearts at the Japanese Yakitori restaurant down the road?

Heart muscle is still muscle, so if there's a viable market, cultured meat can probably make that muscle, too. I've read in an interview with an exec for some cultured meat company that said they could make bone, too. Didn't say they would, but that it wasn't impossible.