You should be able to share landing pages across workspaces. Just put the landing page in a folder and drag the entire folder across
Folders with assets can be shared across workspaces, so my answer to your question would be yes.
You can also take the piece of HTML code which is running behind your LP and create a new one in any of the workspace you wish to.
That's not true. Only folders containing certain types of assets can be shared. Emails and landing pages cannot be shared across workspaces. Just templates.