Steps to follow after resignation on EU Blue Card

[Adhiraj 0]

I'm a non EU national and have been living in Germany on EU Blue card for a year. I joined a new employer in August and planning to quit soon before the probation ends as the work has got very hectic and it is causing health issues and i have a medical condition. What steps I have to follow after resigning - i had some questions around that: 

•  Do I've to inform Agentur fur Arbeit and Auslanderbehorde about job loss ? How much time would i get to look for a new job? My blue card or the zusattzblatt has no employer name on it and it's not connected to the employer.
• I've worked 10 months but if i quit due to health issues would i be eligible for unemployment benefits ?

Thanks.