So it's supposed to rain tomorrow and the next few days after that...

[Major Nikon]

4. I don't think it matters much either way

It isn't going to help much as far as runoff goes, but longer grass means more water used so it will help a little. For most turf grasses you want to take off no more than 1/3rd with each cutting because it keeps the grass healthier and allows the cuttings to mulch back into the soil if you are mulching instead of bagging (which you should). So regardless of conditions it's better to cut your grass regularly. As far as the clover goes, most varieties reset their blooming cycle after you cut them. So if you watch the bees you will probably notice there are more of them immediately after blooming and less after their nectar is depleted. Cutting the clover will cause them to repeat the cycle, so it's better for the bees if you cut after the mature stage.

In dry conditions it's better to keep your grass short(or at the optimum height for the type of grass you have) as less surface area means less evaporation and less water needed to keep the grass healthy.