Hi wof,
When Boeing say 'Max thrust' this means the throttle is at the forward stop and indicates an N1 of 106%
Usually on takeoff the EEC calculated N1 is around the range of 99 -100.1% and this is less than full throttle so in the event of windshear on take off for example the pilot can push the throttle forward to its forward limit and get 'Max thrust'.
So to answer the question on take off set the thrust levers to get the target N1, if the thurst levers are at the forward stop then I would assume something is wrong, to clear the assume temp N1 target you can press the TOGA button to clear it and then you will get the Max N1 limit and the N1 will go to red. (If im wrong some one please correct me)
For your second question...if I remember right you cant dispatch with the EEC in alternate mode but I might be wrong on that one. In flight the EEC in hard alternate mode the EEC use internal software table to calculate mach number thrust thrust settings. During hot days N1 and EGT can exceed its limits.