I do not think the DOJ and FBI can investigate themselves. On top of that, anything less than an independent counsel will be dismissed as a political witch hunt. Okay, how about something novel, give them 90-days to put up or shut up, er, close. They can convene a grand jury and present their cases.
They can and do. Disqualification is generally personal.
There are exceptions. Danforth was brought in to whitewash FBI's handling of Waco.