Answer

In principle, it is moral to represent any person. You are not lying in court; rather, you are making sure that if he is convicted, it is done on the basis of sufficient evidence. If there is an evidentiary gap, then it really is not proper to convict him. It is true, however, that if he himself admits to the lawyer that he did it, then presumably in court he will lie and claim that he did not do it. In such a case, we are dealing with an act where, by definition, there will be no evidence against the murderer, since it was done on his private property. But in any case, if you do not represent him, someone else will. Bottom line, it is impossible to convict him without evidence.
Your last two questions are the same question in different words.