SharePoint PowerShell site permissions
It should be this: Set-SPUser -Identity 'domain\name' -Web http://sp2test/site -AddPermissionLevel Read
What happens if you drop the page from your command?
New-SPUser -UserAlias "test\TestUser2" -PermissionLevel Contribute -web http://test.sharepoint.de/siteAlso, after you add them through the GUI, does your command work to add them to additional sites? Also, dumb question maybe, but are you running PS as a user who has access to add people to the site?
Try adding Add-PSSnapin "Microsoft.SharePoint.PowerShell" It worked for me
Add-PSSnapin "Microsoft.SharePoint.PowerShell"Set-SPUser -Identity 'domain\name' -Web http://sp2test/site -AddPermissionLevel Read