Well, looking at the description of a Not Action from the rules, under combat;
Not an Action: Some activities are so minor that they are not even considered free actions. They literally don't take any time at all to do and are considered an inherent part of doing something else, such as nocking an arrow as part of an attack with a bow.
I would think that it would fall in this category, so it shouldn't be an issue at all. That said, you should probably ask your DM. Different people see it as a different action, and the difference between a No Action and a Swift Action can really kill you, especially if you plan on using Quickened spells, or using the Arcane Armor training feats.
I once played an Eldritch Knight (six levels wizard, one levels fighter, three levels EK) who two-hand wielded an Elven Curve blade. The DM in that campaign said that while I could simply hold the two handed weapon in one hand to cast, switching between 'holding' and 'wielding' would be a swift action. So, I ended up needing to break everything into two turns: one to cast, one to attack. This limited me, since I couldn't do both in the same round, but I was able to work around it. My character was actually a transmutation specialist anyway, so I generally cast all my spells before combat, but before long I found that the Still Spell metamagic feat was quickly becoming my best friend.
EDIT: I found a ruling from James Jacobs, the creative director, on a similar issue: It's for two hand weapons, but I think it would apply.
Well, as you were asking from a RAW answer, here is from the FAQ:
Two-Handed Weapons: What kind of action is it to remove your hand from a two-handed weapon or re-grab it with both hands?
Both are free actions. For example, a wizard wielding a quarterstaff
can let go of the weapon with one hand as a free action, cast a spell
as a standard action, and grasp the weapon again with that hand as a
free action; this means the wizard is still able to make attacks of
opportunity with the weapon (which requires using two hands).
As with any free action, the GM may decide a reasonable limit to how
many times per round you can release and re-grasp the weapon (one
release and re-grasp per round is fair).
—Pathfinder Design Team, 03/01/13
Note the lack of penalties when having the two-handed weapon in one hand. Now to answer your questions:
Are there any RAW that specify whether or not moving is possible with a two-handed weapon held in one hand?
Nope, movement is affected mainly by armor. A wizard is able to run with his staff in one hand, and the game makes no difference in RAW between a quarterstaff and a greatsword, they are both considered two-handed weapons.
Are there any RAW that specify whether or not you are allowed to make a ranged attack with a throwing weapon with a two handed weapon held in the off hand? Is it even possible to do that?
Yep, as in above quote. Free action to switch the greatsword to one-hand, throw weapon as a standard action, free action to grab back the greatsword. Quick Draw would be helpful to draw the throwing weapon though.
Also, this question and other sources seem to indicate that Quick Draw can't be used to switch weapons as free actions.
Best Answer
It is not generally possible
Absent any special feat, class ability, or what have you, it is not generally possible to wield a two-handed weapon in one hand. You can carry one with a single hand, but not fight with it.
Larger creatures can weild smaller creatures’ two-handed weapons in one hand
You can wield the two-handed weapon of a creature one size category smaller than yourself at a −2 penalty. That means you, if we assume you are a Medium creature, could wield a Small two-handed weapon one-handed at a −2 penalty. On average, you generally see a ~1 damage increase for a two-handed weapon over a one-handed weapon, which is not worth a −2 penalty.
Unfortunately, most feats aimed at allowing you to use inappropriately sized weapons without penalty focus on wielding larger weapons. I cannot find any in Pathfinder that work. In 3.5, there were the “web enhancement” kobolds, but as far as I know the Slight Build feature, unique to those kobolds, was literally the only thing that could accomplish it.
Wielding weapons with both hands is typically a good thing
Really must be mentioned: because of the 1½ Str to damage, wielding weapons with both hands is simply better than wielding it in one hand, typically even accounting for the loss of shield or a second weapon.
There may be reasons other than damage that you’re interested in this, but I wanted to point it out.