What are the options to use Ethereum on my mobile (Android) smartphone? Is there a "mist for mobile"?
Not yet. You are referring to DApps running on mobile devices, I think.
There are apps available which offer ethereum-related services like  but they certainly query some nodes via RPC which removes the decentralization aspect.
As of today, there are no light clients for mobile available yet. A mist for mobile has yet to be implemented.
Check this out! https://github.com/syng-im
Syng is a mobile client for ethereum it is an initial release of the Syng client. Mainly to demonstrate proof of concept and encourage developer contribution.
I hope its what you are looking for.
BlockApps provides a RESTful interface to build dapps on Ethereum. You would interact with a deployed strato node just like any other rest service.
WallETH aims to fill this gap - but we are not there yet. http://walleth.org
Bianchetto is a early-stage Ethereum Developer Framework for iOS, it also comes with a SDK for the JSON RPC API, you may want to check it out. https://github.com/bpolania/Bianchetto