In US, most universities start sending out offers around early January. These offers are sent out on a rolling basis. Recipients of these offers are generally expected to inform the universities of their acceptance or rejection by the 15th of April. As many students receive multiple offers, it is common for them to send their decisions well before April 15th. This, in turn, enables universities to extend offers to individuals on the waiting list, should previously extended offers be declined.

I think rankings should not be considered in isolation and scrutinized too much. Many programs consistently remain in the top 10 or top 20 for example, but vary a lot along that list. This does not mean they actually get better or worse. Some ranking criteria are very volatile and tied to factors that may not be of interest to you for example openness to veterans or amount of publications in an area that is not of interest to you. So perhaps evaluate programs based on the tier in which they fall (top 10, top 20, top 30) rather than the exact number. If you then have to account for rankings look at subcriteria provided by rankings, like QS for instance has diversity and employment outcomes sub criteria for ranking as well, which may be more important for international students.