All of those phrases are possible to say, but they have different meanings and usage.
"AT hospital" and "AT THE hospital" usually mean the same thing. They both refer to the physical location of the hospital, and they are used to indicate where someone is located or where something is happening. For example, "I am at the hospital" or "The meeting is at the hospital." However, "AT THE hospital" can also be used to refer to a specific hospital, while "AT hospital" is more general. For example, "I work at the hospital" versus "I work at the hospital on Main Street."
"IN hospital" and "IN THE hospital" are also similar but have different connotations. "IN hospital" usually means that someone is receiving medical treatment or care in a hospital, without specifying a particular hospital. For example, "He is currently in hospital recovering from surgery." On the other hand, "IN THE hospital" implies that someone is talking about a specific hospital. For example, "I visited her in the hospital last night."
In summary:
"AT hospital" and "AT THE hospital" indicate a physical location and can be used interchangeably, although "AT THE hospital" can also refer to a specific hospital.
"IN hospital" generally means receiving medical treatment in a hospital without specifying which hospital, while "IN THE hospital" refers to a specific hospital.