please tell me how much it is possible to make this on iOS?
iOS is a mature OS that comes with Cocoa Touch, a huge library of classes. So, yes it is possible. And the question of possibility shouldn't be attached with the word much
. Either something is possible, or something is impossible. Don't take it as how much. If it is possible, you can do it.
how about background network connections and SQLite?
Of course, this is possible. Like android, there is a rule in iOS that only your main thread can interact with the UI, and all other heavy tasks should be attached with other threads. You will use Blocks
to accomplish this kind of functionality.
Also is it possible to send local push notifications in background?
Yes, it is quite possible. Have a look at the following document.
Local and Push Notification Programming Guide
Do have a look at http://developer.apple.com/, here you find a lot of documents related to the tasks you have asked in your question.