will a NAT Gateway costs even if no data is transferred?

Yes

different between NAT Gateway and NAT Instance?

NAT gateway is a managed instance which is highly available. NAT instance needs to be configured, maintained by the user, but user has more control over the device

what is FSx for Lustre?

FSx is a managed file system used for compute intensive workloads

can two private ip s communicate by peering connection?

Yes

can one internet gateway shared across multiple VPC?

No