Re German offensive, it will depend on the situation. Vulnerable beach ? Attack. Allies close to their cadre limit ? Attack. Need to extricate valuable units ? Attack. Don't forget that shifts for artillery and troop quality can bump up that 1-1 attack. And if you can force an Allied stack to retreat and thereby disrupt, it might be worth the loss of a step to blunt a potential Allied attack.
This is a good point. Actually, I was so concentrated on getting the rules down that I kind of overlooked the automatic victory conditions against the british...five 3-step-to-cadre reductions is probably the easiest route to victory for the Germans. I bet that Tiger battalion helps toward this, although in this game I sent it into Caen to defend the city and wasn't able to use it to it's best potential in hindsight.
One other is when you have the British player in clear terrain. The terrain West and NW of Caen is clear terrain. I pull the Germans back to the edge of the bocage/clear terrain line. When the British are sitting in the clear terrain I attack with 12SS and Pz Lehr.
I'm going try this on my next run through. I had been sending everything towards Caen and Carentan (the Germans had taken back Carentan around turn 8 and needed help).
Unfortunately this is exactly what the game proposes, an hopeless attritional stalemate turn after turn passed the first week or so. Historical perhaps, but kinda boring.
I will admit the action slows down a little after the first few turns and you have to grind it out more, but I haven't found it to be boring.