1. You don't have the latest VMware Tools present on an ESXi 5.5 node.
You would have to use the download page.
Watch out, VMware Tools 10.3.5 are not supported on ESXi 5.5, VMware Tools 10.3.0 are.
2. This depends.
If you are using the VMware Tools that are present on an ESXi node, you can just use the Update-Tools cmdlet.
If you are using an external installation file, you will have get it into the VM's guest OS, and then trigger the installation.
Brian did a post on that, see SILENT INSTALL OF VMWARE TOOLS FROM THE COMMAND LINE
Also note that this command will be different depending on the type of guest OS running in the VM.
The easiest way, imho, would be to create an ISO containing the installation file.
Mount that ISO on the VM.
And then with Invoke-VMScript, trigger the upgrade command.
This will NOT work for an installation from scratch, since Invoke-VMScript relies on the VMware Tools running.