There are four general questions for anyone who believes that Jeremy killed his family.
(1) Why did DCI Jones remain so convinced of Jeremy's innocence even when doubts were raised?
First of all, since he died before the conviction and his own records have not publicly been released we have scant evidence of the basis for his positions were. We don't even know if he still maintained such positions till his death or changed his mind because he did not go on record- he had no reason to do so. After the trial be might have given interviews had he lived and we would have an idea.
All we knwo is that police who work with him say he was stubborn and once he got something into his head you were unable to change his mind. If he did maintian his position to his death and that is why then it means he did it because he was stubborn and refused to admit error. But to be fair we don't know how convinced he was of Jeremy's innocence at the time of his death.
(2) Why did Julie remain by Jeremy's side for weeks whilst suspecting (or knowing) that he was a murderer?
Because she loved him
(3) Is it really plausible that Jeremy, if he did kill his family, has a complete absence of conscience and the ability to fool all the professionals who have talked to him to evaluate his mentality, has comprehensively passed a polygraph test, and has convinced mike tesko and various other people that he has talked to extensively that he is innocent of killing his family?
yes. It is easy to fool people, particularly when they lack enough information to make a valid assessment of the situation or they are inclined to believe certain things. The people he has fooled tend to be people who do not trust police and are willing to believe things that most don't think make sense. Some also have been fooled into believing claims that upon scrutiny turned out to be false because they lack the ability and/or desire to carefully scrutinze the claims. What I have found is that many blindly believe claims some of which has been refuted by evidence available on this website. Many of the statements and other documents actually debunk claims from Jeremy's website and that Mike parrots.
(4) Why has mike tesko (if Jeremy did kill his family) been inventing discussions with informant(s) from EP for years?
I can only venture a guess and that would be- drumroll- for attention. Only Mike knows whether he actually believes Jeremy is innocent and makes up lies to help Jeremy or Mike is simply using this for his own purposes. Some people live to have a cause. There are much more worthy causes he could devote his time to but worse ones as well such as terrorism.