1. You have not followed up the demands properly.
You should have made a demand for settlement of your salary arrears, PF and gratuity payments by sending a legal demand notice after your resignation if the employer had not entertained your personal letter.
The emails sent by you would not be recognised as correspondence, hence it is always better to have the correspondences in writing and sent by registered post so that this can be produced as evidence at the time of the dispute referred before concerned authorities or court.
2. You can give a maximum period of 15 days for settlement of the due to you, but make sure you send the demand notice by registered post instead of adopting the fancy email correspondence alone.
3. Without any evidence for the accident or medical certificate for the illness due to the accident you cannot claim any compensation, your email communication in this regard is not a substantial evidence for getting your claim settled.
4. Bering a doctor by profession, you may not be covered under labor laws, hence you may have to either file a recovery suit in the civil court or file a writ petition before high court.
As per section 8 of the Payment of Gratuity Act, 1972:
If the amount of gratuity payable under this Act is not paid by the employer,
within the prescribed time, to the person entitled thereto, the controlling
authority shall, on an application made to it in this behalf by the aggrieved
person, issue a certificate for that amount to the Collector, who shall recover
the same, together with compound interest thereon at such rate as the Central
Government may, by notification, specify,] from the date of expiry of the
prescribed time, as arrears of land revenue and pay the same to the person
entitled thereto :
Provided that the controlling authority shall, before issuing a certificate
under this section, give the employer a reasonable opportunity of showing
cause against the issue of such certificate:
Provided further that the amount of interest payable under this section shall,
in no case exceed the amount of gratuity payable under this Act.
6. The calculation for this is: Gratuity = Average salary (basic + DA) * ½ * Number of service years
7. The Gratuity calculation formula is: Gratuity = (15 × last drawn salary × working tenure)/30.
8. The compensation for accident claim is different to that of gratuity payment.