So is "egy" optional in a sentence like this? Does using it alter the meaning or connotation in any way?
Yes, it's optional, though it's more often used than not.
Why is "igen, ez egy szék van" incorrect? When is it incorrect to use "van" in a sentence that uses "is"
Is ‘van’ optional here?
No, it has to be omitted. You omit "van" and "vannak", whenever the predicate is a noun like here or an adjective.