2. Some routes between Asahikawa and Asahidake/Tenninkyo are not direct, so one should make a change at Higashikawa Michikusakan-mae. Is it easy enough to transfer? Do buses arrive to and leave from the same stop? Is there on Internet any information about timetable between Higashikawa Michikusakan-mae and Asahikawa?

No, this transfer is not necessary anymore. All bus connections are no direct.

May be you are aware of bus connection between Asahidake and Tenninkyo? We are reflecting upon visiting both hot springs in a day. Say, if we pass the trail between Asahidake and Tenninkyo, can we get back to Asahidake by bus to catch the last bus to Asahikawa at 17:30? Or is it a bus to Asahikawa from Tenninkyo itself? And can we go from Asahidake to Tenninkyo at around 2 p.m. by bus instead of hiking?

Correct: All bus connections are now direct.