Since Margaret supposedly was under a death sentence herself because of her crimes ...
Wait... WAS she?
She was certainly pushing the boundaries, linedancing at the edges of the Laws, trying to get the WC to revisit and revise their Laws, seeking more "social justice" and protection for mortals, general activism and interventionism by the WC.
We know she was on the Warden's "watchlist."
But I didn't think she had ever been
convicted of Lawbreaking, or gotten any death sentence (at least, not from the WC) ... ? Being on a watchlist is VERY different than being under a death sentence!
... Why was the child Harry so difficult to trace until Justin came on the scene and adopted him?
Presumably, because Justin was behind the act of hiding Harry.
... Given everything that surrounded Margaret's death, why didn't he look into Malcolm's more closely? ...
I presume he looked into the matter as closely as he could. He was "on mission" when Malcom died, there was likely
at least one Sunrise to wash away magical traces.
But above all -- he was a working Warden: a cop. Like Murphy was. And (like Murphy was) he was subject to oversight. While Luccio may have sympathized/protected him, he already knew an "enemy" had "invaded the Senior Council itself."
So Morgan's investigation & action was limited (like Murphy's was) by what he could get away with, given an "enemy" who had such oversight.
... If Morgan thought that Harry was truly infected, why didn't he just give him the chop when he was under the Doom? ...
Morgan didn't
think Harry
is infected.
Morgan
feared Harry
might be infected.
Morgan was "stress testing" Harry, trying to see if Harry showed signs of using Black Magic or being Nemfected, trying to force Harry into needing to use the shortcuts-to-power those represent, the weakness of character they display.
I think Morgan would have been... more comfortable? ... if he could have proven Harry to be a BlackHat. Far better, for brawler-type wizards like Morgan (and Harry (and Eb)) to face a clear opponent upon whom you can unleash all your powers, than to have a viper slithering 'round in your own nest!
But in the end, Morgan couldn't
quite bring himself to execute a child (and then a very-young man) who kept showing he DID have the self-restraint to avoid using black magic, every time he got pushed or tempted that direction.
... He also knew very well that Luccio had murdered LaFortier, he covered for her and that is why they were after him in Turn Coat. Also he was instantly on the run when that happened, so when did he have time to make a journal entry? ...
Actually, he knew Luccio
didn't kill LaFortier. He knew that Luccio was somebody's
tool, a mind-thrall
used to kill LaFortier... in other words, just another victim (but one custom-made to take the fall, and to disrupt the WC).
It's an interesting parallel to how Toot & "the Za Lord's Guard" were also "just tools" and bore no animus for killing Summer Lady Aurora. Titania's wrath was wholly-reserved for Harry (she could have off'ed the little faeries in a heartbeat, if she had wanted to).
But even "on the run," Morgan would have had moments of downtime, periods where he was bandaging, eating, drinking, resting, etc. He was using the Summer Boon to be safe from all scrying, after all. And he evidently thought that his thoughts and conclusions on "the Dresden Situation" were of tactical or strategic importance to Luccio and any other allies, so it was a priority to get them down in writing (all too likely he'd die being captured!).