Apartment's in Stuttgart

It is not clear from your post what you want to know.
I recommend you read related discussions on this forum (and elsewhere) first and then come back with more specific questions.

The salary is a pretty average income so it should be enough. The difficulty is in finding a good place. Foreigners often have it even harder than others. This is not always racism per se but renters of good apartments really have the choice of who they rent to. Being foreign or self-employed or even looking a bit too alternative can make it difficult when there are others with great jobs and education looking like a model family out of an advertisement. People will tend to rent to the people they feel the most secure with; having good jobs and that they know they can communicate with. Maybe your employer can give some assistance. If someone in the company knows of a good place and can recommend you to the landlord then it can help your chances.