1) A hospital is a place. You could perhaps say Hospital is the place where people get treated... or even better Hospital is the place for treatment... or the place to get treated, but in all these cases "The hospital is the place" is still better.
3) Idiom. Or you may say I will be back two weeks after my marriage, after I finish my diet, and so on, but you really need to specify after what. You may also say I will marry in July, and will be back two weeks thereafter, where thereafter = after that.
4) From dictionary.reference.com:
The form alright as a one-word spelling of the phrase all right in all of its senses probably arose by analogy with such words as already and altogether. Although alright is a common spelling in written dialogue and in other types of informal writing, all right is used in more formal, edited writing.