Updated : 23/06/2015
As an unemployed jobseeker, you are allowed to stay in Austria for at least 6 months.
You will be allowed to stay longer, even if you do not have any income or unemployment benefits from your home country, as long as you can show that you are genuinely looking for a job and have a real chance of finding one. You can prove this with, for instance, copies of job applications, invitations to interviews or positive reactions to your applications.
YES — you're right. If you're looking for work, you can stay without registering your residence for up to 6 months.
NO - as long as you have registered as involuntarily unemployed with the public employment services, or have begun vocational training. In these cases you retain your status of worker - at least for six months, if you worked less than a year. The same applies if you are temporarily unable to work as a result of an illness or accident.
In any case, you retain the right of residence if you have sufficient resources and comprehensive sickness insurance or if you have lived in the country for over 5 years (permanent residence).
YES — Since you are temporarily unable to work due to illness, you can stay in Austria for as long as this condition continues.