Hiwin Lubrication

[JAZZCNC]

Does anyone know what HiWin (HG-30mm) recommends as the preferred lubrication?

Lithium soap-based grease is what they state in manuals, so basically any lithium grease.
Grease is often used on milling machines because it doesn't contaminate the coolant as much as oil causing what's often called "tramp oil" on the surface. Oil lubed rails are better if high feeds are being used but do cause more Tramp oil.

Does the HiWin carriage has this foam insert inside the lubrication gallery?

No, they don't have any foam or filters inside. I think you can buy things like this which replace the end caps, they even have self-oiling options which I think are little oil tanks that fasten on the ends.