You need to use the passive with born (to be born).
Your sentences would be correct like so:
1) He had already been born when I reached the Hospital.
2) This is where I was born.
3) Your father came to hospital but that was before you were born.
4) He was born in India.
The past participle born is one of the two different past participles from the word to bear (borne & born). However, when referring to birth, born is used and can only be used in the passive form. Therefore you can only find it in combination with the verb have as an auxiliary verb in perfect tenses:
- He has been born.
- He had been born.
You cannot omit the verb to be in your sentence, it is required to form the passive. Born cannot be used in and active phrase, not when you're talking about birth.
To form active sentences when talking about birth, you use borne. However, with that past participle, it is the subject who is performing the act of giving birth while the object is the one that starts his life.
She has borne two children.
This website contains some solid information on the difference between born and borne: Borne vs. born - Grammarist