Why didn't Saruman kill the Ents himself?

[Zigûr]

why did Saruman attack Rohan so prematurely with his army?

It didn't seem premature at the time. He was not expecting to have to assault a fortification like the Hornburg, because he did not think Théoden would recover. He didn't know about Gandalf's activities in Rohan, healing the King and freeing Éomer from imprisonment, until Wormtongue arrived at Isengard, by which time it was much too late. He'd already defeated Rohan twice at the Fords of Isen, after which time he must have assumed that the Hornburg would not have the manpower it did, nor that Gandalf would have time to find Erkenbrand and bring reinforcements to their succour, nor still that the Huorns would come to destroy the remains of his army.

why did Saruman not fight the Ents himself when they attacked Isengard?

He did. He spilled fire and boiling steam on them from his forges and had his orcs attack them with arrows and axes - but that's the problem. Saruman had spent his power in machinery and soldiers. He could not have emerged from Orthanc and gone toe-to-toe with Treebeard in the ring of Isengard. All his power was bound up in his devices and slaves. Also, Saruman knew that the Ents could not harm Orthanc itself, so it would probably make more sense to hide in the tower than risk harm by coming out and fighting the Ents in person. Note that Gandalf recommends that Treebeard fill Isengard with water until it stops draining away, because he suspected that Saruman might have escape tunnels dug beneath Orthanc should he have needed to leave in a hurry. So Saruman did try to fight, but only with the means which he possessed by then.

That is at least how I read the situation.