Xcode database usage confusion
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I am new to iPhone app development and have a question about storing data. I've spent quite sometime learning about core data but still confused about the concept of persistence store.

What I understand is that core data is just a way of managing the data you downloaded from an external database. But given that core data is backed by SQLite, does that mean there exists a SQLite db in-memory while running? If so, does that mean when I use core data it will be more effective if I download a huge data set at start? But what about apps such as twitter or Facebook that require constant update of data, is a straight $NSURLConnection$ sufficient in these cases? If core data is used, will the extra overheads (i.e. data objects) be of any burden for such frequent request of update?

I would also like to find out some common ways of setting up an online database for iPhone app? Is it usually MySQL servers with a homemade Python wrapper that translates the data into JSON? Any standard server provider would provide the whole package? Or open source code? 

Many many thanks!