I am pretty sure they are taking about taking money from people who work for foreign entities but are Americans. FARA means Foreign Agent Registration Act.

That would be incorrect. As Wikipedia puts it:

"The Foreign Agents Registration Act (FARA) is a United States law (22 U.S.C. § 611 et seq.) passed in 1938 requiring that agents representing the interests of foreign powers in a "political or quasi-political capacity" disclose their relationship with the foreign government and information about related activities and finances. The purpose is to facilitate "evaluation by the government and the American people of the statements and activities of such persons.""

There is nothing in those emails to indicate that they are not citizens is there?

Eh? The subject of the email is "Foreign registered agents". In fact, if you actually read through it, there's an earlier thing where they talk about a policy that was considered:

"The policy would be to not allow any currently registered foreign agents (those who register with FARA) to contribute or raise for the campaign. If someone terminates their registration, they would be allowed to contribute or raise for the campaign."

Note how shady it is that if someone terminates their registration (and thus the campaign can deny knowing), they'll take their money, even though they know they're a foreign national.

Read the whole thing. The whole email thread is about taking money from foreign nationals. If they were talking about American Citizens, why would there be a discussion at all?