My group went on the 4 day hike in late March of this year, the tail end of the rainy season. We really got all sorts of weather, but 3 of 4 days were not rainy. You do run the risk of being damp (and Day 2 at the highest altitudes can be chilly) but during the sunny periods, it wasn't as hot as during the dry season - I think preferable for hiking. Seems like the temps ranged during the day from high 50s to low 70s. As far as stuff to bring, think layers and remember warm clothes for the evenings and nightimes (extra fleeces, hats, gloves, etc.) and waterproof dry bags for your clean clothes. Some people had gore-tex rain suits, remember to get the breatheable stuff.
Re: altitude sickness, I arrived a day earlier in Cusco than my group, and appreciated the extra time. I did take Diamox, but the first day in Cusco was still slow going - just don't expect to hustle around or overeat.