If it's Disintegrate? No, you still can't cast it.
Distintegrate's casting requirements are the following:
Components: V, S, M/DF
- V = Verbal. This is no problem, as the Sorceror can speak.
- S = Somatic (hand gestures). Still Spell removes this requirement, so being tied up is not a hinderance.
- M = Material. This is a specific item that you have to have in hand, usually from a Spell Component Pouch. The problem is with his hands tied, the Sorceror has no way to take the necessary item out of the pouch to use it. Due to this, the spell can't be cast.
That's as per this rule:
To cast a spell, you must be able to speak (if the spell has a verbal
component), gesture (if it has a somatic component), and manipulate
the material components or focus (if any)
The feat Eschew Materials would remove the Material requirement, at which point the spell could be cast.
You can cast any spell that has a material component costing 1 gp or
less without needing that component. (The casting of the spell still
provokes attacks of opportunity as normal.) If the spell requires a
material component that costs more than 1 gp, you must have the
material component at hand to cast the spell, just as normal.
A spell that did not have a M component in its stat block wouldn't have that issue, and you could use just Still Spell to cast it.
Can you Aim It With Your Hands Tied?
Distintegrate's text says this:
A thin, green ray springs from your pointing finger. You must make a
successful ranged touch attack to hit.
Still Spell removes the Somatic component of casting the spell, but nothing in it's text says that it removes the need to aim the spell or the mechanism by which you do that. So by RAW, you would still have to use your finger to aim the spell, with your hands tied.
If your hands are tied in front of you, it wouldn't be that hard. If your hands are tied behind your back, it's going to be pretty tricky as you can't see what you're pointing at. In that case I'd use the rules for Total Concealment (50% chance to miss whatever you're aiming at). This raises the issue of figuring out how you're tied up, which is quite possibly something that wasn't thought about if nobody described it and a Use Rope skill check was used to do it.
The other interpretation is that the finger pointing is just part of the Somatic component (hand gestures) required to cast the spell. If you interpret it such that it is, then Still Spell also removes the pointing requirement, and you would aim some other way. Probably by eye contact. You'd still have to make a ranged touch attack, as per the spell description.
In either case, penalties for being tied up might apply depending on how well you're tied (a fully bound character is Helpless and has an effective Dexterity of 0, which is a -5 on the attack roll). If they just secured your hands, a lower or perhaps no penalty would apply, that would be a DM judgement.
All Area of Effect Spells are Three-Dimensional Unless Otherwise Specified
Note the use of the phrase many-layered in the Web description. All areas of effect in 3.PF are fully three-dimensional unless, such as in the Blade Barrier spell, a different area is specified. Web does not specify that it isn't three-dimensional and as such takes up the entire space of its area between the two anchor points.
As far as that not making physical sense...friend, it's Pathfinder. This is pretty high on the 'making physical sense' scale. Rules don't translate well to physics.
Best Answer
I'd say "greatness" is whatever the caster is trying to encourage their targets to accomplish in that moment.
Essentially, the verbal component is you trying to give them a motivational speech for 1 minute, meanwhile weaving in a magical component that consists of the mechanical effects of the spell.
It doesn't involve any element of compulsion, so even though you've given them an inspiring speech encouraging them to do the thing, they could go do something else with the buffs you just put on them. It's just flavor.