Make a beeline for something means you go straight to something. For example: John made a beeline for the candy section as soon as he walked in the grocery store. The child made a beeline for the toy. Falls short means not reaching a certain standard or goal. For example: John's attempt to finish his report tonight fell short. Our plans for the summer fell short. His skills fell short of the required standard. Falls flat means to be unsuccessful. It's usually used to refer to jokes. For example: John's knock-knock jokes fell flat. The speaker's attempt at levity fell flat. I don't think I've ever heard people use "fall overdue" before, so I can't help you there. I also don't know how to explain grammar, so somebody else will have to answer your grammar question. But "it falls overdue a week" makes no sense to me.