I believe that Core i5 will only be desktop and I think Core i3 will be as well and will be like the Pentium Dual Cores of the Core i family.
As for the laptop versions, there has been no real info on them yet but there will probably be a variant of each. Not like the Core i7 laptop though. Thats just shoving a desktop CPU into a small space.
Sorta kinda. There will be Core i7s and Core i5s and Core i3s for each: desktop and mobile, but given the new naming scheme they may or may not be related. The high-end desktop Core i7 currently out is Bloomfield-based, but the new Core i7 mobiles (and possibly some desktop models as well) will be Clarksfield/Lynnfield based.