A stopped (deallocated) VM is offline and not mounted on an Azure host server. Starting a VM mounts the VM on a host server before the VM starts. As soon as the VM is mounted, it becomes chargeable. For this reason, you are unable to start a VM after a trial has expired.

A network security group works like a firewall. You can attach a network security group to a virtual network and/or individual subnets within the virtual network. You can also attach a network security group to a network interface assigned to a virtual machine. You can use multiple network security groups within a virtual network to restrict traffic between resources such as virtual machines and subnets.
You can filter network traffic to and from Azure resources in an Azure virtual network with a network security group. A network security group contains security rules that allow or deny inbound network traffic to, or outbound network traffic from, several types of Azure resources.
https://docs.microsoft.com/en-us/azure/virtual-network/security-overview