Working remotely working for a Canadian company while living in Berlin

I'm thinking of asking my current employer in Canada (in software tech) to give me the option to work remotely for a while, and chances are they'll say yes. (currently I'm on a work permit in Canada)

I wonder what things I need to consider when doing this in terms of economics, legal matters, taxes, insurance, etc. More specifically:

1- I'll be staying my Canadian taxes in full. Is there some sort of German income tax that I would need to pay as well? If yes, how much.

2- I'm not a Canadian citizen and normally I can stay max 90 days in a 6 month period in Berlin. What are my options to stay longer and would those affect my taxes situation?

3- How about insurance, would I need to pay separately for my insurance in Germany? Would I need to have that considering the extended health coverage that my current employer offers? (although not sure how it would work for a long stay abroad)

4- Any other obvious thing I should be mindful of in terms of economics, legality, etc. ?

You may be allowed to stay in Berlin for 90 days in a 6 months period, but that is a VISIT visa, not a WORK visa - your are NOT allowed to do any paid work during such a visit (not even remote for a foreign employer or client).
To do this legally, you need a FREELANCER visa. (A work visa would not suffice, since you have no German employer.)
Of course, any income generated while staying in Germany is subject to German income tax and other deductions (most importantly for freelancers: German health insurance).
If Germany has a tax treaty with Canada, there might be regulations in it that reduce the occurence of double taxation. Check it! (In most cases - except USA - the rule is you pay tax on your world income where you live and not where the employer is or where the money is paid out.)
To complete the related paperwork (all in German language), you should engage an accountant and tax consultant.

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