I would like to know which SharePoint servers I should install workflow manager. do I need to install the wf manager on a server that doesn't have sharepoint? or do I need to install it on web servers with sharepoint installed?
You can install workflow manager on non sharepoint server or you can install it on sharepoint server as well. It's depend upon resources(server, hardware etc).
Important thing is, if you have more than one server...if you install workflow manager on one server then install workflow manager client on all remaining sharepoint server.
For more information please the below technet.