Does Apple watch need a carrier or can it send emergency via iPhone

1. I am a high risk category for falls. Can an SE Apple watch with GPS only, send an emergency message to family and emergency services using my iPhone XR which is always on me?
2. I have no need to use a watch for general communications, so have no need for any cellular phone. I think.
3. LIving in Australia, Apple says that only Telstra, Optus and Vodaphone are the only eligible mobile phone carriers that are allowed to link your Apple watch and iPhone for an emergency call to go out. Their rates are triple what I pay now and I am an aged pensioner and cannot afford this 'luxury'. They also charge an extra $5 per month for this privilage.
4. So, is there a way, staying with my current mobile carrier, that I can use a new model SE watch with or without my iPhone, strictly for FALLS and emergency notification to family and emergency services?

Any help in plain language would be appreciated please. I cannot seem to find any on the web.

Thanks,

Peter