As you noticed, Destruction is pretty straightforward. Each cast and while continued casting, you will increase skill, but this has a caveat: only if you are attacking someone. If you're fizzling your spell in the middle of town, it's not going to increase it.
Alchemy is also straightforward: each potion created will increase your skill. As dpatchery notes, eating ingredients for effect determination will also increase your skill by a small amount.
With Enchanting, each enchant (or disenchant, as LessPop_MoreFizz notes) as will increase skill. dpatchery also notes that you can increase your skill by recharging items with soul gems.
Restoration, namely the healing spells, only increase skill if your health is below its maximum. The others only work if you're in combat or near hostile enemies: this includes spells like Steadfast Ward.
For summoning spells (essentially most things in the Conjuration school), you won't get a skill up for the summon until you enter the range of hostile mobs and, in the case of summoned creatures (like the Atronach and the Familiar), they do some damage. With bound weapons, entering range of hostile mobs is all that's necessary to gain Conjuration skill; however, using them in combat will increase their appropriate weapon skill, not Conjuration.
Alteration and Illusion spells that are targeted towards messing with hostile mobs need hostile mobs within range to skill up. Buffs, like Oakflesh, don't increase skill without hostility as well. Others, like Candlelight and Muffle, are recastable without hostility but only increase skill by a small amount.
SOLUTION!!!
I can confirm that I too had this issue on the PS3. No matter what I did I could not get above 22% in my items with same information you have given.
I went into game data on the ps3 menu and deleted the game data and the game update for Skyrim. Launched the game and let it patch and reinstall the game. I then went straight to an enchanting table and with no enchanting gear I could create +25% alchemy gear using Grand Gems alone.... I edited a section on Wiki about bugs and stated that I confirmed a solution to this problem.
Best Answer
Long answer
Yes, percentage increases should apply to the effects of mods on your skills, assuming they're changing the rate in the sensible, straight-forward, native way that Skyrim already uses to determine improvement rate.
Internally, Skyrim has a number attached to each skill so that the developers could tweak the rate at which they improve on a per-skill basis. These numbers are in the data files rather than the engine. This allowed them to set a rate for, say, Alchemy's improvement, see how it affected gameplay over time, and tweak it up or down without having to recompile the entire game from scratch. The various bonuses you can get from Standing Stones and other sources are designed to layer on top of these to give the advertised increase, no matter what the number.
What levelling-rate mods change is this number. Since they change the same number that Skyrim was already using in the skill-rate equation along with the things that give a percentage increase, the percentage increase is applied to the new value just fine.
As we can see from opening 2x Skill Increase in TES5Edit, that's exactly what this one is... er, waitaminute...
We've found a bug! And a novice modder who hasn't done their research.
The left pane shows the list of records that manage skill data. The right pane shows two yellow-highlighted lines: those are the changes the mod makes compared to the base game. You can see that
Skill Use MultandSkill Improve Multare double their original values.What we should be seeing is
Skill Use Multbeing double what is listed inSkyrim.esm, butSkill Improve Multbeing left alone. As we can see on the UESP article on Skill Levelling, the first is the actor value that controls how much XP that skill gains when you use it, whileSkill Improve Multdetermines how much XP you need to get to improve it to the next level. What this modder has done is double the amount of XP you get each use, but then also doubled the XP you need to reach the next skill point! Net effect: this mod has zero effect on skill levelling.(Also notice that entry for
AVAbsorbChancewith the light green background without the selection dashes at the bottom in the left-hand pane. Green means "no change". That means their mod has a "dirty" change, where it duplicates the base game value without meaning to. This is a major source of bugs and unintended mod conflicts, since when other mods are legitimately intending changing it this mod just changes it back to default for no good reason. Another sign of a new modder. It's very easy to do accidentally, and sometimes due to bugginess the Creation Kit itself inserts dirty records when you save out a mod, but experienced modders learn how to check for this and clean their mods before releasing them.)This mod would be easy to fix given the tools and knowledge (in fact, I can fix it with just a few clicks in that TES5Edit window I screenshotted), or re-created properly from scratch (since it's only a few clicks in the Creation Kit), but teaching either is beyond the scope of a Q&A answer. It would also leave the modder without feedback and the others downloading it afflicted with a mod that is both ineffective and has dirty edits, so the better course of action is to comment and inform the modder of the error. They do have the tools to fix it, and can do it at the source so everyone can benefit from a functioning mod.
Short answer
Yes, skill increase mods will stack as you'd expect with Standing Stones that give a percentage increase – they'll multiply the percentage against the rate that the mod sets.
The mod needs to work properly first, though.