Good day,
If it is possible to restore the same virtual machine to two different resource groups,
Yes, You can restore VM several times as new VM, and you can move VM to a different RG, which mean that you get multiple "copies" of the VM in different RG
A VNet is limited to a single region. A virtual network does, however, span availability zones.
is the network isolated in resource groups?
Yes, but you can use VNet peering to connect virtual networks.
https://learn.microsoft.com/en-us/azure/virtual-network/virtual-networks-faq#can-a-vnet-span-regions
Does this mean that virtual machines A in first resource group can have the same IP address as virtual machine B in second resource group?
Do not confuse between internal IP to public IP.
Two VM in two different vNet can have the same internal IP, but two VM cannot have the same public IP.
And, can both virtual machines run at the same time without mutual influence?
Just like you run a machine at your home without any influence on a machine in my home. Two VM which are not connected under the same vNet or any other relations so not have direct influence on each other.
I need VMs accessible from outside, with access to Internet.
This is not related to most of what you asked before, since I spoke about internal IP inside each vNet. If you need to connect to the outside then you will need for example a public IP, and in this case you cannot have 2 machines with the same public IP
Check the link regarding VNet peering. It might solve some of your needs.