I've said this before, but it bears repeating:

As to foreign corporations and election money, here's what Citizens United said:

We need not reach the question whether the Government has a compelling interest in preventing foreign individuals or associations from influencing our Nation’s political process. Cf. 2 U. S. C. §441e (contribution and expenditure ban applied to “foreign national[s]”). Section 441b is not limited to corporations or associations that were created in foreign countries or funded predominantly by foreign shareholders. Section 441b therefore would be overbroad even if we assumed, arguendo, that the Government has a compelling interest in limiting foreign influence over our political process.

Slip op. at 46-47. Obama was wrong.

What is the legal definition of "principal place of business" in regards to the law?

Funny you should mention that, because the Supreme Court just decided that question in Hertz Corp. v. Friend. I was going to write about the case but there really wasn't anything I can add. The court's decision—that a corporation's principal place of business for purposes of diversity jurisdiction is the state containing its "nerve center," i.e. operational headquarters—is so overwhelming sensible that I couldn't think of a thing to add.

I don't know where Lenovo's headquarters is. Various reports describe North Carolina as its headquarters and as headquarters for its U.S. operations; this indicates that there is a Beijing headquarters, though it isn't clear whether that's headquarters for Lenovo's China operations or Lenovo as a whole. In any litigation (assuming Hertz has broad application, which seems likely), the actual location of a corporation's nerve center is a question of fact that would have to be established. See Hertz v. Friend, 559 U.S., slip op. at 18-19.