You are looking under the Purchased link under Quicklinks on the right-hand side of the iTunes store home page for re-downloading it on your Mac ? If other music appears there (music can't be re-downloaded in all countries), then is it hidden : hiding and unhiding ? You should also be able to copy it from the iPad to your Mac's iTunes via File > Devices > Transfer Purchases
Home sharing is for streaming content from a computer to another computer or device, or for copying from computer to computer, it won't stream or copy from an iPad.