Does a trial judge have any duty to ensure that a defendant's right to counsel of choice is protected?

When a defendant asserts his right to self—representations does the trial judge have any duty to see that the self—representation is meaningful?

Does the trial judge have any duty to ensure that all papers and representations presented to the court are properly signed, properly before the court and are not presented for any improper purpose pursuant to rule 11(a) of pleadings, motions, and other papers and representations to the court, 11(b), 11(b)(1), 11(b)(2), 11(b)(3), and 11(b)(4)?

Does the trial judge have discretion to disregard established case law? Can the trial judge disregard or alter the rules of Criminal Procedure and rule 11 procedures on an ad hoc basis to fit a particular case or circumstance?

Does a trial judge have a duty to protect a defendant's right to counsel of choice?