Just back also from May 28th - June 5th stay. Small World is completely enclosed, they did put benches along the wall for people to sit out of the sun. There are signs up stating that the ride is closed for refurbishment.
Didn't do any early mornings this trip, so can't answer the bus question. From previous trips, I think they start running about 45 mins prior to early opening, maybe an hour not sure.
The heat was bad, the Memorial day weekend was in the upper 90's with no clouds or rain. We did finally get some afternoon showers later in the week, by that time, I think the rain was welcomed by most.
The crowds were pretty heavy, heavier than this same week last year. Did e-night on June 2nd and that was good, no waits except at Space Mountain. They were running just one side, so the wait was about 20 mins.