You could probably make Arresto Momentum relatively safe by having it choose between the caster's frame of reference and the earth's (at the caster's position) based on whichever results in the spell doing less work. It's still dangerous, obviously casting it on someone else's moving vehicle would be a bad move, but it avoids making anything go "zoom" in a privileged frame of reference.
Arresto Momentum itself looks very safe on first view, and nobody warns about, say, casting it while inside a moving vehicle
Every single casting of Arresto Momentum ever was performed on a moving planet, which resulted in no issues. It's possible that casting from inside of a moving vehicle to outside of it might result in problems, but I strongly doubt that it'll do anything which would seem bizarre from the caster's frame of reference.
I don't think Rita Skeeter is good evidence. It would not do for Quirrell to have Harry notice an unexpected, strange burst of magic when he's trying to quietly kill someone; Quirrell would have found a way to suppress it, if it had existed. (It's also possible that her Animagi transformation suppressed the effect.) The absence of the burst of magic in Harry's parents' deaths, on the other hand, has led me to an inverse suspicion to yours...
It is notoriously difficult to trail someone who is wearing the True Cloak of Invisibility, with added anti-detection charms because apparently the Deathly Hallow just wasn't enough.
Or, Harry is summarizing a wide variety of observations on the topic of puberty in a pithy and relatively un-embarrassing fashion. We don't know Harry's actual basis for claiming that he hasn't yet begun puberty, but his comments on the subject are just a little too flippant to be the complete truth.
The problem is that "bypassing the Interdict" is not, on its own, useful; it's only valuable if Harry happens to have written notes on powerful magic spells that are censored by the Interdict. Apparently, there's a loophole allowing Interdict-restricted material to exist (wizards can keep notes for themselves, implied by chapter 23), but it seems unlikely that Harry would be able to get ahold of much of it. (Possible exception: Bacon's diary? Quirrell didn't think Bacon found much of interest, but he could be wrong.)
Related: since Muggle physics can apparently contribute to powerful magics (see: partial transfiguration) would the Interdict apply if Harry ever wrote a physics book? What would the Interdict do if a Muggle happened to accidentally write (presumably as fiction) the details of a powerful magic spell? Can Muggles read Interdict-restricted works?
Time-Turners are in frequent and authorized use by a fair number of students, as well as Dumbledore himself and possibly other staff members. Any such ward would be constantly triggering, for no particularly important reason. Even if one exists, I can't imagine that Dumbledore pays much attention to it.
Dumbledore is only looking for Hermione. There's no reason for him to be much interested in Harry's magical devices, beyond proving that they aren't Hermione. The portkey was only mentioned because it was a part of Dumbledore's body search; the Time-Turner, presumably, wasn't on his body.
Inferi appear to be common knowledge; they're cited in casual contexts in chapters 70 and 78, by Lavender Brown and the narrator respectively.
Just so you're aware, it's fairly easy to dump the script files from Umineko if you'd prefer to read it that way. There's also an auto mode, which is irritatingly slow, and a skip mode, which I used to skim through the art after reading the script file.
You might prefer the story of the Higurashi visual novels to the anime, and the English release has a configurable (and pleasantly fast) auto mode.