Does calls between 2 azure resources in same regions adds to network bandwidth cost?

This is ingress vs egress as discussed here. In general, within the same data center (region) it is ingress but across regions and outside Azure are egress. It depends upon the service whether you get charged for both but in most cases ingress is cheaper than egress as you're staying inside the local Azure network.

As far as cost goes it is complicated so it depends upon your resources. You should use the price calculator to get a better idea. But, based upon my understanding and your screenshot.

• Azure functions charge by CPU usage and not network bandwidth as that is part of the triggers, not the function itself.
• App Services (which is probably where you are hosting your APIs) are charged by the tier used and hours running.
• VNets are free by themselves but cost money if you're using gateways.

Note that the above does not include other services you may also need such as storage and any customizations you've made.

Assuming all the above is in the same region then you should just be paying for the app service hosting and the runtime of the function. But, again, you should check the pricing calculator and check your billing.