Why did he throw that?

[Belin]

It did always seem a bit odd to me as well. But imagining that Wormtongue understood what the palantir was would make Saruman less prudent than Denethor, who was using his for ages before anyone caught on. I have trouble believing that Wormtongue spent any considerable amount of time in Saruman's study (the wizard doesn't strike me as the sort of person who would appreciate others poking about amongst his tools and treasures), so he may not have even seen it before.

Besides, we don't know what else Saruman had in there. It wasn't designed to provide his minions with artillery, after all.. perhaps the palantir was simply the most likely large, heavy object to catch Grima's eye, and the chances that, in his state of rage, he stopped to think about what it was and how Saruman used it are not that great. But he did understand a big rock dropped on your head from a tower would probably kill anyone.

Eowyn? Eh... I don't really see any evidence that his desire for her (I wouldn't call it "love") was in any way bound up with wishes for her well being. He was interested in her body and her status, but since he'd figured out that at this point he didn't have much chance for either, he probably hated her as much as he did Theoden.