a) Petron by Indus motors is fine, Equal to oils avalible in similar price range.
b) Your not bound to use Toyota Motor Oil to retain warranty.
c) Any damage caused by getting your can maintained outside wouldnt be covered under warranty.
d) By maintaining your car outside the dealership, Your cars warranty does not gets void, Just that if any damage is caused by getting it maintained outside is not covered under warranty.
e) You can use any oils that you like for your car, Just make sure it is meant for your car and doesnt damages it.