Germán motorized units are doubled attacking towns?
No, see the end of the first paragraph of 17.1.2 (Special Barbarossa Campaign Rules). This is explicitly not allowed. The Motorized being double strength when stacked with a panzer division only occurs against clear hexes on turns 1-3.
Are mech units halved attacking cities without city defense markers?
On turns 1-7, yes. Starting turn 8, no. 17.1.2, third paragraph.