When to use "есть" in possessive constructions
My understanding was always that when indicating possession, есть is sort of an optional word. So:
У меня есть стул.
У меня стул.
are both correct.
Am I incorrect about this? I've come across several sentences that were counted wrong with есть or wrong without it, and I'm honestly not sure whether to flag them as mistakes or not.
It is not an optional word.
If you want to express the existence of said object in your possession, you use есть.
If the existence is not questioned (like "I have long legs"—surely, having legs won't surprise anyone) or the identity of the object is stressed ("Careful! He got a gun!"), you do not use есть. In practice, this often happens when your sentence describes a property of an object using an adjective or expresses quantity. Then, chance is «есть» should not be used (you still need to check what the sentence is really about).
Here, I mean that in English you say that you "have" things for all kinds of reasons. For example, "I have a brother" does express the existence of a relative while, from a Russian POV, "I have 3 brothers" or "I got a smart brother" is more about quantity and quality. "We have a grey cat" focuses on a characteristic if said by an average Joe but it might focus on possession if said by a pet shop owner (or by a person who has cats but of whom it was not clear if they had a gray one).
You do not use «есть» with body parts and illnesses.