If a person has been arrested already, can the federal government bring up
additional felony charges while that person awaits trial?
Yes, they can bring related and unrelated charges as long as they are within the applicable statute of limitations.
And if so how long does the government have to bring up the charges
The general statute of limitations for federal offenses is 5 years. This means that formal charges or an indictment must be filed with 5 years of when the offense was committed. 18 U.S.C. 3282. However, there are numerous exceptions to this rule.
For example, Congress has chosen longer periods for specific types of crimes – 20 years for the theft of art work; 10 years for arson, for certain crimes against financial institutions, and for immigration offenses; and 8 years for nonviolent violations of the terrorism-associated statutes which may be prosecuted at any time if committed under violent circumstances.
Also, tax fraud has an extended statute of limitations. Under 26 U.S.C. § 6531, there is a 3 year statute of limitations for criminal violations of the tax code; however, there is a 6 year statute of limitations on: willfully attempting to evade or defeat any tax (§ 7201), willfully failing to pay any tax or file any tax return (§ 7203), filing a false return (§ 7206(1)), aiding or abetting the preparation of a false return, claim, or other document (§ 7206(2)) and submitting false documents (§ 7207).
Embezzlement is subject to the general 5 year statute of limitations.
However, this where a statute of limitations analysis gets extremely facts specific. Certain circumstances can toll or pause the statute of limitations, such as a defendant being a fugitive, if the crime is a continuing act, or if it was part of a conspiracy.
Check out the Congressional Research Report titled Statutes of Limitation in Federal Criminal Cases: An Overview for a more robust discussion of these issues.
And will the charges be in one trial or in a separate trial?
Again, this a fact specific inquiry for a judge to decide. However, they can be joined if they are "are of the same or similar character, or are based on the same act or transaction, or are connected with or constitute parts of a common scheme or plan." Fed. R. Crim. P. 8(1). See also Fed. R. Crim. P. 13 (allowing a judge to order that separate cases be tried together if they could have been filed as one case in the beginning).
Say a man is arrested for embezzlement, and while awaiting trial the
arresting agency found evidence of tax fraud. Could the agency charge
the man with tax fraud and embezzlement in one trial, or would it need
to be two separate trials?
Assuming the statute of limitations is not an issue, they could (and probably would) be made part of the same trial; however, a judge is not required to so.