Insight and Precision is not included since that seems more like modifiers than anything else.
They're not, any effect involving perceiving or manipulating magic directly falls under those. A Meditation to get more info on enemy magic items would be Insight, for instance.
Athleticism / Scouting:
Leave No Trace (control of force input to not leave visible traces behind)
This would be Scouting, but it's valid.
Generally there would be precision stuff in this category, but I have no idea what would be useful after we get Grip.
Almost all the stuff that's useful beforehand? Anything involving stuff like running, jumping, and so one would be unaffected by Grip, and Grip doesn't help lift bigger weights, so a Rote or Meditation for that would also be valid.
Administration:
Forgery Detection, Speed Comprehension (of documents), Report Summarisation (might have overlap with the previous one)
These are potentially valid, but would come under some stuff.
Diplomacy:
Greatest Need / Want Detection, Light Prayers (either to highlight favourable points of Audrey, or to highlight provocative points; or remove spotlight as needed), something to find cultural red lines.
Highlighting favorable stuff in Audrey is already very much how Cloak of Grandeur works. Figuring out what people want is definitely a valid Prayer, avoiding cultural issues is probably under higher levels of Gift of Tongues.
Scholarship:
If feasible, some kind of Prayer Of Tongues equivalent for translating theories and frameworks into more easily understandable ones?
Logical Fallacy Detection? (Something that evaluates the merits or lack thereof of an argument faster)
Those aren't really things, I don't think. Some suggested ones people have already mentioned include enhanced memory or boosted knowledge in specific areas.
Scouting:
Trace Detection, Group Strength Estimation (might fall under Tactics or Insight instead)
Tracking is something you can do already, though you could get better. Group strength estimation is definitely Tactics, and can also be done already, though you could get better.
Tactics:
An extremely budget form of PtV perhaps? (Only accounts for what we know and what we have, and must have goals explicitly specified)
I'm not sure what you're asking for here. I don't always catch the abbreviations.
Light:
Demonstration Aid (what Aalis used, to physically highlight things we want highlighted or to construct diagrams in the air)
You can probably just do this kind of minor effect. You need a plan for what you actually want it to do that amounts to more than a minor special effect to make it a Prayer.
And on a side note, does Grip allow for walking on (generic unstable surface), by treating it as one discrete object and spreading the force of Gravity over the entire area especially when combined with Perfect Footing?
Perfect Footing already does that pretty much as well as anything can. Grip of Samson on its own helps, but not as well.