My sickness allowance is not enough to survive
With paid sick leave shorter than 6 weeks at 100% and extended paid sick leave around 70% salary indefinitely, that is exceptionally bad financial planning. Sorry to be blunt, but if you are so much in debt that you cannot survive on 70% of your salary you have a problem. And it's not your workplace. Your financial planning is gambling on you being lucky and not getting sick or injured.
I want to go back to work after my sick note ends. However, the doctor is saying I need more time to recover. Is it ok to go back to work as soon as the sick note ends when I am still in recovering phase?
Matter of fact you have to go back to work when you sick note ends. You cannot just decide to take sick leave yourself. However, if your doctor says that recovery is needed, they should give you another sick note as long as it's needed. That is up to your doctor to decide. For some kinds of injuries they might not give you an absolute paper, but rather a list of things you are not allowed to do. For example not lift heavy objects above 10 kilos if you had a back injury. If your employer can accommodate that (lets say you work in a warehouse but they give you an administrative office job for the duration) then you have to work, if not (lets say you work in construction with no alternative) then you are on paid sick leave. So go ask your doctor what they meant by "recovery" and how that works with sick notes.
My current employer knows my ICD code.
They probably won't care. Since it is not relevant to how they treat you or all the paperwork involved, I doubt they even bothered to look up what it means.
My illness recovery time is a very slow process, will it create a problem?
No, as long as you have proper documentation and communicate to all involved parties, that should not be a problem. People get sick. That's not nice, but really not that much of an exception either. Companies deal with it regularly.
Should I listen to the doctor and recover fully?
now I am really worried that they will take my sickness as a reason and fire me
They are not allowed to. Period. Nobody here can guarantee you that they won't try, the same way that we cannot guarantee you that you will not be in a car crash or be robbed or be framed for a double murder you never committed. But it's highly unlikely. I mean they don't pay you while you are out sick, that is on your health insurance, so what would even be their motive to fire you? You cost them nothing, the only thing they have to gain from firing you is a lawsuit that they are bound to lose. You being an expat, I guess they went to great length to hire you in the first place so it's double unlikely they will want to get rid of you. Firing you for being sick would be illegal and stupid. Not saying that combination does not exist, but it should be super rare.