Is it Constitutional for a District Court Judge to Hold an accused in an alleged criminal proceedings indefinitely in detention without TRIAL when the accused has pleaded NOT Guilty?

Can any accused have a direct appeal of right without a TRIAL or the accused pleading guilty to the said allegation?

Does the U.S Constitution permits a District Court Judge to knowingly impose a sham Counsel for the defendant just to aid the unconstitutionality action of a bias court? OR

Does the professional conduct code permits any appointed counsel who is in conflict with the client to openly act like a prosecuting counsel against the said client?

Is it Constitutional for a District Court Judge to Hold an accused in an alleged criminal proceedings indefinitely in detention without TRIAL when the accused has pleaded NOT Guilty?