How far down must a tooth cavity be before a crown is no longer a proper treatment?

Near the pulp. If the cavity is in close proximity to the pulp of the tooth then in addition to a crown the tooth will likely need a root canal. If the tooth has developed a deep crack that extends below the pulp and into the root then the tooth will likely need to be extracted.
Depends. There are a number of factors to determine whether a crown should be placed or not. Crown height vs root length, diameter of root, above/below bone height, whether crown lengthening can be done, anterior vs posterior. See your dentist...He/she will evaluate the situation.
Deepth isn't ?? Depth itsnt necessarily the concern it's the mount of missing tooth structure ratio to healthy to structure. Depth is a concern if it creates a nerve exposure or undermines the enamel.