What kind of charges can be brought up for a secret inditment?

Answer 1

First of all, an indictment is only "secret" while the Grand Jury is hearing testimony on it. Once it is issued and served it is no longer 'secret.'

Occasionally "Special Grand Juries" are empaneled to hear charges of a particularly sensitive nature, the leakage of which might obstruct or ruin ongoing investigations.

An example might be organized crime and racketeering indictments, or national security issues could be another. However under the US system of justice once the indictments are handed down and served on the accused the charges are no longer secret and the cases are tried in open court.