Have corporal, and especially capital punishment been Halachiclly suspended in any way? If yes, is it limited to specific time periods or circumstances? Specifically, when Jews have sovereignty over their legal system (as is the case in Israel), would they be obligated to implement the Torah penal code? Would that include corporal and capital punishment?

Corporal and capital punishment, as well as some other aspects of Halachic jurisprudence, are dependent on the status of "Mumchim" or "Semuchim", that is, judges who receive authorization to judge froma line of tradition stretching back to Moshe himself. This authorization may take place only in Eretz Yisroel, therefor, with the Galut (exile) the Semicha process was lost. According to some opinions (including Rav Yosef Cairo's (the author of the Shulan Aruch) the Semicha can be reinstituted by a large group of Torah scholars in Israel. Not everyone agrees with this view, and the chance of its implementation is iffy, to say the least. At least for the forseeable future, the Torah penal code is in hiatus. If and when the Semicha is reinstituted, there still may be factors that would cause the Sanhedrin to forgo some of the penal code if they deem fit.