I would like to know if I can use a VPN gateway that already exits and work with one vnet, to use it in other vnet that is in other resources group to connect to the resources that exist in the other resource group
Please refer to hub and spoke concept.
No you can’t.
What you can do is setup vnet peering en tunnel that vnet over the existing gateway.
Other thing you can do is use the same vnet but add an address space to it
You would have the VPN gateway in a hub network, and your other VNETs being your spoke networks. Connections between the hub and spokes are done through VNET peering. This gives you that connectivity without having to create gateways between different VNETs, or to on-premises.
Yes.
With two vNets peered, you can choose to allow one vNet to use the Gateway in another vNet.
Look up ‘gateway transit’.