Since everything falls down, it seems to me that gravity acts as some sort of natural super-Rego effect. If so, surely Rego magics might redirect gravity (to reduce gravity would be Perdo I imagine), though I don't know what the base effect level would be.
Would it be possible to create a ReAq spell that causes water and other liquids to fall in a different direction (eg upwards) while all other materials still fall down, within the range and duration of the spell?
Or a ReHe gravity spell to upset archers shooting arrows?
ReCo to make people fall sideways towards a hazard?
Have a quick look at the paragraph on natural movement on A&A p.25 Change in Place: Motion. Falling is part of that movement, which has inanimate objects strive towards others of their own level. It is not caused by any kind of magic.
That being said - yes, all of the example spells you describe are fully capable of being created within the Hermetic paradigm; the basic concept is that downward motion is a property of the object, not of any invisible "gravity" field. As such, if you want to modify the motion of an object, you must affect the object. You can set up Rego Terram wards that would cause all rocks in, say a room, or a circle, or a structure, or whatever, to fly upwards. However, once they left the effect of the field, they'd fall back down. As such, the end result of that particular example would be to expel all rocks to the top of the ward where they'd hover about, just on the outside of the spell.
The basic assumption here is that Rego wards affect everything within them (AM5th, pg. 114), or that cross their boundary, even after the spell is cast. This is explicitly listed in the wards section, but by process has also been more-or-less acknowledged for other effects, as well. As such, the whole "you must target the thing you are casting on" verbage in the core rulebook is a bit...well...outdated and not quite clear. For Area of Effect spells (ie, the Room/Circle/Structure/Boundary effects), they end up affecting every appropriate thing within them for the duration, even if that thing wasn't in them to begin with.
Most RegoX TeFo's have some variant of "move object in an unnatural way" - you'd use that base guideline as the base, and then slap on the appropriate adders to make your spell. You can also port guidelines over from the ReCo section, as those seem to be the most exhaustive.
Medieval physics makes little distinction between gravity and specific gravity/density.
"You see, my apprentice, everything tends to fall or float to its proper level: Terram at center, Aquam next, then Auram, then Ignem, and theoretically Aether. Even within Forms, you see this; mix grains of lead, iron, and tin, and shake, and the lead will sink and the tin float, and the iron settles between them. The same is true of liquids, as alcohol or oil floats on water, so too some vapors on others, and the purest fire above the cruder flames."
Apparently the natural specific gravity of living bodies is roughly that of water.
Let me second what others have already said, and answer to the specific questions.
There is no "gravity" in the medieval paradigm, but a "natural tendency" of the four elements to move towards their proper resting place: Earth to the very bottom, then Water above it, then Air, and finally Fire on top of everything else (note that Fire is the "lightest" of all four; "lighter" in fact than Air).
This means that Hermetic Magic cannot affect "gravity", but must instead affect the individual objects, either:
with Rego, to shove them directly to where the caster wants, regardless of their "natural motion",
with Muto, to change their "natural motion" property e.g. to make earth behave as a mixture of air and water, and thus float,
with Perdo to destroy the "natural motion" property, so an object just "hangs" there where it's left, whether in mid-air or deep underwater.
with Creo, by creating unnatural objects that have a different "natural motion" than natural ones. Note that it's Creo, not Creo(Muto), according to ArM5, despite the note in TME contradicting this (and many other basic principles of Hermetic Magic).
All these effects are "unnatural", and thus inevitably last only as long as the magic sustaining them.
Definitely. But the catch is that you must target the objects themselves, you can't create some "mystical field of force". Of course, with T:Room, T:Circle etc. you automatically affect all objects within a given area, so in these cases the distinction is mostly academic.
That helps somewhat.
"Natural Motion" property indeed. An intrinsic property rather than an intrinsic action, hence not related to Rego.
The medieval paradigm is not intuitively obvious.
At least this time I wasn't confusing what Rego and Muto covers.
And to close the loop, there is no "gravity" form, as it was explained, each objets/target must be affected by the appropriate form.
If you wanted to create a type of "0-Gravity field", it would be a Mu (as Fafnir nicely explained the difference between Rego and Muto regarding natural movement) An, Aq, Co, He, Te (so with a +4 requisit modifier), D: Ring (+2), T: Ring (0), R: Touch (+1) Base effect: 3 (I am basing it MuTe: 1, change one property of dirt, +2 to affect metals), so MuTe(An, Aq, Co, He) 30.