Regarding a longer leave

Dear Ana, 

according to the following official information

https://www.sachsen.de/en/3070.htm

You can leave for upto 12 months without losing

your permit. Regarding the other questions I am sure you have to notify your employer and they (HR) should know if someone from the state needs to be notified. If you do not have an official address in Germany any more you may run into problems. I would suggest you change your official address in Germany to someone you know and trust such that official snail mail is still reaching you. At least some administration will not send emails only  (taxes ) and for sure not send them abroad. 

The German 'entsendegesetz' may apply if you are also working abroad. 

All the best

Frank