1.Only if you are born in Indian jurisdiction you can have birth certificate issued from that local corporation office under register of births and death

2. No. You can get origin certificate not birth certificate. 

The birth certificate is issued by tge hospital where you were born. It cannot be reissued. However, the birth certificate issued was an authentic one so you should have no problem in issuance of other documents based upon the birth certificate.

A child who is born to any one of Indian parent(s) abroad can acquire Indian Citizenship by Descent and is required to be registered within a year's time. A Birth Certificate is issued by the Embassy to the child after registering his/her name as an Indian national. A separate passport can be issued to the new born as detailed under Passport Services. The following documents are required for Birth Registration:

• Birth certificate from local hospital
• Birth Registration Certificate from the local provincial authorities with notarised English translation.
• Birth Registration Application Form signed by both the parents.
• Affidavit to be signed by both parents.
• Copy of bothparent’s passports

2) has been made mandatory by Government of India for registering online the birth of a child as an Indian citizen. For detail information applicants are requested to visit the website of Ministry of Home Affairs http://indiancitizenshiponline.nic.in

3) However, if the parents of the child return to India to settle, the birth can be registered within 60 days from the date of arrival of the child to India, after which the delayed registration provisions are applicable.

Following is the procedure under Births and Death Registration Act for obtaining birth certificate …

1. Apply to municipal authority as per the date of your actual birth. Municipal authority will give a certificate that no such birth is registered on that date.
2. Submit an application to the Executive Magistrate/Tahsildar/MRO with proof of temporary birth certificate for direction to municipal  authority for birth certificate  on the said date with following 
3. A notarized affidavit stating that your birth took place at Jeddah on the said date and the same is not registered.
4. No birth registered certificate issued by municipal 
5. Notarized affidavit of mother and father (if alive) stating that you birth took place on that date and it is not registered.
6. Executive Magistrate/Tahsildar will give direction to municipal authority for issuing birth certificate.
7. Take that direction to municipal authority and apply for birth certificate  on said date.
8. You will get required birth certificate on payment of Rs. 50/- fee to municipal 

Dear Client,

Apply to municipal authority as per the date of your actual birth.

Thank You.

The birth of every child born in the Kingdom of Saudi Arabia to Indian parent(s) is required to be registered with the Embassy of India, Riyadh or Consulate General of India, Jeddah depending upon areas of jurisdiction.

The birth of the child is required to be registered with the Indian Embassy within one year of the birth.  In case, the registration of the birth could not be done for any reasons, one of the parents of the minor may meet the Consular Officer with a request to register the birth detailing the reasons for not registering the birth on time, alongwith following documents.

1. Online registration of the birth of the child born abroad under section 4(1) of the Citizenship Act on the website https://indiancitizenshiponline.nic.in/IC_4_1_tab.aspx, duly attested by the consular officer.
2. An application detailing the reasons for not registering the birth within one year of the birth of the child.
3. Applicants are required to fill online application form at https://embassy.passportindia.gov.in and carry a printout of the filled in application form duly signed by both parents [child’s thumb impression (left thumb for male & right thumb for female) should be affixed in the signature box].
4. Annexure D to be signed by both the parents and presence of both the parents or either parent with passports of both the parents at the time of submission of application;   OR   Annexure C in case of single parent or the other parent not available for reasons mentioned in para III of the Annexure.
5. Copy of Birth certificate issued by Ministry of Civil Affairs along with its English translation in original.
6. Birth Registration Certificate in Original.
7. Three recent passport-size photographs of 3.5 cm x 4 cm with white background (For more info, please go to photo specifications).
8. Photocopy of both parents’ passports (original to be shown for verification).
9. Photocopy of both parents' Iqamas (original to be shown for verification).  A copy of printout showing validity of Iqama from Ministry of Interior website (https://www.moi.gov.sa/wps/vanityurl/en/ps/pps/query-iqama-expiry-service) may also be submitted.
10. Atleast one of the parents should have spouse's name endorsed in the passport.
11. Prescribed fees.

1. Since, your birth place is out of India, then you cannot get a birth certificate from the office of Registrar in Delhi.

- Further, as per rule ,in order to get Indian citizenship for a child born to Indian parent in a foreign country, the birth of the child is to be registered at the nearest Indian Embassy/Consulate and thereafter , and the parents can apply for issue of an Indian passport for the child. 

2. Yes, you should approach the Indian Embassy after submitting the proof of birth in SA , with the other documents like proof of residence , identity proof , and passport .