No you don't need to let them dry between washes. You can lanolise the cover if you like but I don't Depends if you have a big wetter or not though. If you do have a big wetter then lanolising it will help with it's waterproofing but it will eventually leak if it's saturated.

For liners I use microfleece from spotlight. Look for stuff called little additions (or similar, i think they changed the name of it).