Best to get the car seat. Taxi doesn't need but indeed it's more cost efficient and more convenient sometimes to take normal Grabcar. U can buy Doona stroller as it can also be used as a carseat frm newborn onwards. More ex than normal stroller but a gd investment for those travelling via private hire cars or when u want to rent a car.
It is safer to get a car seat (but not compulsory in taxi). In the long term it will be more cost-efficient to own your own car seat and take grab instead of taxi or grab family (expensive for the type of car seat they provide - not the safest option - and not always available).
if taxi, you can carry ur baby without car seat but if its under grab/gojek all the private hire u need it
U need car seat if taking private hire. Carrier is meant for carrying not for car ride..