Transfer from articleship in last year

I don't think you are correctly following ehat the ICAI is trying to say via its norms.
Here are the relevant norms:

-Medical grounds requiring discontinuance of articles for a minimum period of three months (on production of a Medical Certificate issued by a Government Hospital).

Now the meaning of this is that from a recognised hospital( government hospital) you will have to produce a 3 months inpatient certificate and that will be if you're having a fracture that goes on for 3m or have a brain problem.
So no just on the basis of you feel that you are requiring parental care is not an eligible enough

If there is a brain problem and produce a certificate from government hospital related to the same, will it be mandatory to get new registration after the expiry of 3 months or the new registration can be done right after the receipt of acceptance letter of transfer from the institute.

Legitimate certificate that your condition is as such that you require to be inpatient for next 3 months from a Government hospital will be sent along with your handwritten application stamped and approved by your Principal along with the necessary transfer commencement forms to e ICAI, they will then look into the matter and may grant you transfer.