Regarding your last point about foreign money being used in the U.S. election, you should familiarize yourself with the concept of "soft money" and political action committees.
And the outside entities can bypass the US organizations entirely. There's no law against someone from another country buying political TV ads in the United States.
PACs still cannot accept foreign money, though obviously it is easy to launder. NY real estate companies are a popular money laundering method for this kind of stuff.
And the outside entities can bypass the US organizations entirely. There's no law against someone from another country buying political TV ads in the United States.