Officially, you have to show original photo ID (along with the ticket) when entering the airport as well as when checking in. For Indonesians, this is their national ID card; for foreigners, this is their passport.

Practically speaking, however, Indonesian airport security is usually more relaxed about these things than most countries.

I suggest you cover all bases by bringing a copy of your passport, your German ID card and a short note explaining in Indonesian why you don't have your original passport. Something like this:

Saat ini, paspor saya di kantor imigrasi karena KITAS masih diproses. Atas perhatiannya, terima kasih.

(Sorry if my Indonesian isn't great; Google Translate is your friend).

At the hotel, you might have to give (not just show) a copy of your passport to hotel reception when checking in. I've never heard of a hotel refusing to check in a guest for this reason.