(1) I'd figure 300-400 miles per week, unless you're in really good shape. Really, really, good shape. And carrying very little in the way of gear.
(3) Costs are all over the map. The lowest estimate I consider reasonable is $15/day. You might need to double it, depending on what campsites cost this year. (Or multiply by 20 if you have to motel it in a beautiful, scenic, touristy area.)
(4) AIUI, most of the slides occur in rainy weather. Wait 6-8 weeks for the end of the rainy season, and check the road status then.