If I get the iPhone 5S, can I transfer all info from the iPhone 4?

And I mean All info

Of course you can

Yes you can

Yes! If you have icloud turned on then you can backup your content to it and when you are setting up your iphone 5s just choose the restore option and all of your content should be put on your iphone 5s

Yes, absolutely.
Here is the link to the support page from apple on how to do this.
There are two options; iCloud or iTunes.
Hope this helps.

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