I have only ever been able to share templates. My general "workaround" is I download the HTML of the email template I'm looking to hang onto, then dump it into the new workspace. Takes a bit of time, but generally works well overall! Just be careful when you have images that they are shared as well.
Another workaround that one of my colleagues suggested can be used would be as below:
For eg: landing page in Design Studio
1) You may want to create a sub folder in the folder where that asset is located
2) Clone the asset and place it in that sub-folder
3) Now select the sub-folder and drag it to the desired workspace and location (Please be sure that if it’s the landing page, you will have to place the sub-folder in the Landing pages section of the other workspace and not under Forms or Emails in Design Studio)
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.