Question: There seems no possibility to fly from Yazd to Esfahan, so we must go there either with train or bus. Do you know the excatly info? And for the bus, how is the exact deparure time? Besides: How long it takes from Persepolis to Pasargadae, and which Sights is has?
Answer: Yazd to Esfahan is only 3-4 hours drive so no airplane flies between these two. Train departures are only at night, as far as I know. And "frequent" departures of bus are available, something about each 1-2 hours a departure.
Pasargadae is a UNESCO-recognized small ziggurat-like monument of Cyrus the great. From Persepolis to pasargadae is about 1 hour. If you want to go there from Shiraz, it will take about one full day to visit both Persepolis and Pasargadae, then you can continue the route to Yazd and visit Abarkouh on the way as well. You should take private car to these sites.