This will depend on local and company customs (and any laws/regulations where applicable). In my opinion:
No, do not answer (most) mails.
Answering mails (or communicating in general) is work. You are officially unfit to work, so you don't.
To address your points:
I am sick and all my projects are blocked. These projects all affect
the entire company, and there are external collaborations included as
That is not your problem, but your manager's. It is a fact of life that anyone can become unavailable at short notice (suddenly quitting, servere illness, serious accident...). If there are no contingency plans for that event, that is not your fault.
Several departments are asking me for help, but there is only me in my
role and I couldn't sleep because of my manager.
See above - your manager should arrange for someone else to take over.
That said - if your manager or the person(s) taking over for you have specific questions so they can better pick up your work, and there is information that only you have, you might want to help. To cite an extreme case, if you are the only one who knows some admin password, you should definitely answer mails about that.
Even better, if you feel you are able to, you could volunteer the information you think is important (by phone or in writing, as you like) and pass it on. That shows that you try your best to help where you can.
Also, the mail where you volunteer the information is a good occasion to explicitly point out that you will not read your work mail during your illness. :-)