How can I let my app popup something like Cydia's "Reloading Data"/"Loading Data" (like this)?
Is it a public API by Apple?
How do I call this?
Can I specify which image to display instead of the Loading indicator?
First of all, it's neither a public, not a private Apple API - it's a custom control.
Second, why don't you just use Cydia's implementation itself?
Third, if not, there are alternatives as well.