Can a judge remain on the bench with a pending corruption case against him?

You have multiple parts to your question, so here is a breakdown of each:

First, a judge can remain on a bench if there are pending charges if the administrative judge or judicial commission does not remove him.  To remove a judge, the commission needs to receive and rule on the complaint.   Judges have been removed pending charges if the Texas Judicial Commission decides that their removal is warranted.

Second, a warrant can be issued for someone who's already in jail.  The warrant is usually on a new charge.  If a person is held in jail on that warrant and later pleads guilty to the offense, they are entitled to any credit for days that the served in jail as result of the warrant.  For example, if a defendant is in jail on a new charge, and then a warrant is issued for an older probation revocation case, he would get credit from the first day of arrest for the new case.  He would only get credit on the older probation violation case beginning on the day the warrant was served on him in jail.  As far as rights... the defendant has the same rights as anyone else as prescribed by the code of criminal procedure and jail standards. (This would include arraignment on the new warrant, rec time, access to an attorney if they are indigent, etc.)

Third, if you have a warrant in one state and are arrested in another state two years later, then you have the right to resist extradition.  Resisting extradition usually just results in delays and aggravation of the prosecutor who will eventually being making a recommendation in the defendant's case.  Texas has interstate agreements with most states such that if the State can prove the defendant is the one in the same (i.e. via picture or prints) who is wanted, then the other state will turn the defendant over to Texas officials to be transported back to Texas.  Most states have similar agreements through their governors' offices.  A defendant may want to resist extradition, but it usually only serves to delay the inevitable.    

Under the laws of all states in this country a person is deemed innocent until proven guilty of a criminal act. As such, the judge can remain on the bench despite a corruption charge against him.

A warrant can be issued against a person already in jail from another county or state. The rights of the person with the warrant issued is to contest extradition. If you are arrested in one state and the warrant on the other state pops up, the person can contest extradition.