The billing process depends on the service provider. The insurance company does not control it. Whether it is going to be a direct billing or not depends entirely on the billing practice of the doctor or the facility you visit. Most big hospitals and doctors bill directly to the insurance company. However, in exceptional cases, the patient may receive the bill from the provider. Generally, if the bill is large like for a surgery etc, then it is likely that the doctor/facility will bill directly to the insurance company.
Please refer to this link for further information: Travel Medical Insurance With Cashless Pay or Direct Pay Policy
Insurance rates are regulated by law. You can't find the same insurance plan for a lower price anywhere else