Once, we deregister in October, we will be informing health insurance co abt the same. We will anyways pay insurance premium for October. If we incur any medical expenses (for our kid, franchises is 0) towards end of October can we still claim it in November and request them to payout in our accent in new country?
If you've paid the premium for October and then incur medical expenses in October... of course you can claim them back. Even after the end of October!
After all, bills will often arrive several weeks after the doctor's appointment or hospital visit (I've just received a hospital bill dated last November)!.
As for where the insurance company pays the reimbursement, that you might need to ask the insurance company. Usually they pay out to swiss bank accounts but you can't be the first person with this problem so I'm sure there are other possibilities.
If you go to live in the EU you may have to pay for an extra 3 months cover, unless you can show insurance in the new country or free NHS healthcare for example.