As for Powershell: you have a very limited number of cmdlets. Usually you differentiate between SP cmdlets (for server) and SPO cmdlets (for Sharepoint Online). Here is a full list of cmdlets: http://office.microsoft.com/en-001/sharepoint-help/introduction-to-the-sharepoint-online-management-shell-HA102915057.aspx
To connect to SPO you need the Sharepoint Management Shell and connect-sposervice: http://technet.microsoft.com/en-us/library/fp161392
As for the initial problem: have you checked with the site content types and site features if there's something that could help you?