These are different questions.
They can petition a congressman on their own behalf, but lobbying on behalf of their home nation's interest would probably require them to register under FARA. They can lobby on behalf of a foreign government if they register under FARA.
They can contribute to an issue-advocacy PAC. They cannot contribute to a candidate. This has been decided by the existing case law and it is explained on the FEC website.
The relevant paragraphs are:
- Despite the general prohibition on foreign national contributions and donations, foreign nationals may lawfully engage in political activity that is not connected with any election to political office...
- In a decision that was later affirmed by the Supreme Court, the U.S. District Court for the District of Columbia ruled that the foreign national ban “does not restrain foreign nationals from speaking out about issues or spending money to advocate their views about issues. It restrains them only from a certain form of expressive activity closely tied to the voting process—providing money for a candidate or political party or spending money in order to expressly advocate for or against the election of a candidate.” Bluman v. FEC