Defining good caching scenarios
IMHO It is a good idea to cache api results if you don't need real time data. If you don't care that you won't see new data for an hour, then by all means cache it for an hour. So for your first question, you just need to ask yourself: "How fresh does the content need to be for my application?" and implement caching accordingly.
For the second question: I don't see a lot of value in caching content if it's only been manipulated in simple ways. At that point you're using up space in your cache and not getting a lot of value. But if there are database, or other api calls being made using that data, then yes they should be cached using a technique similar to the above.
If you're that worried about processor load (the only reason to cache content after manipulation) you're best bet is to look at something like Varnish or CloudFront.