1. I forgot to mention and as is Rummann understood correctly, that reason for using reduced stiffness for axial tension is that we will get less tension from analysis (due to less stiffness/restraint).
2. Negative temperature will produce tension near restraint (like slab supported on heavy walls).
3. What is the use of building? Is it a car park where you need to apply temperature to all the structure? Otherwise as Umar and you already pointed out, its the top slab where you need to consider differential temperature between top and bottom slab and thats not possible with ETABS 9 atleast.
4. Yes, tension should be checked on appropriate combination with other loads and that is 1.2D+1.6L+1.2T plus other loads if you have. If still you are getting tension that means it will be carried by modulus of rupture + steel only.
5. I would recommend you to use reduced stiffness of 0.25 and then also subtract the tension capacity of concrete (equal to half of 0.62(f'c^0.5)xthicknes in Mpa), half because slabs are restrained as per ACI.
6. For compression, cracking modifier should be increased but walls are quite stronger in compression. So just use 0.25. This is your separate model for temperature analysis. Keep it separate from lateral analysis where you might be using 0.7 or 0.35 modifiers for shear walls. Or it will affect the distribution of lateral forces to columns as you pointed out. But keep in mind, that is the real situation, if temperature cracks walls before earthquake hits, walls would be very weak transferring lateral forces to columns. Others can shed light on this more.