Arcane Spell Failure
Arcane Spell Failure only applies to Arcane spells that have Somatic components, yes. Wearing any armor, even armor you are not proficient in, has no effect on spells that are not Arcane or Arcane spells that do not have a Somatic component.
Still Spell is a (very expensive) way around Arcane Spell Failure, yes.
There are far, far cheaper ways. A +1 twilight1 mithral2 feycraft3 githcraft4 full-plate with thistle-down padding5 has a 0% Arcane Spell Failure for just money, specifically 15,600 gp. Saving yourself a feat and a +1-spell-level cost on most of your spells is easily worth that much.
Using mage armor or a Chain Shirt (+1 twilight mithral, mithral fey-or-githcraft with thistledown, etc) of some kind would be much wiser, though, since it is a lot of money. AC is not that valuable for most spellcasters. A dedicated gish (warrior-mage) probably wants levels in prestige classes that mitigate or ignore Arcane Spell Failure anyway.
1 Magic Item Compendium, reduces Arcane Spell Failure by 10%. +1 equivalent, magic.
2 SRD, reduces Arcane Spell Failure by 10% among other things. 9,000 gp for Heavy Armor, mundane.
3 Dungeon Master’s Guide II, reduces Arcane Spell Failure by 5% among other things. 500 gp, mundane.
4 Dungeon Master’s Guide II, reduces Arcane Spell Failure by 5% among other things. 600 gp, mundane.
5 Races of the Wild, reduces Arcane Spell Failure by 5% among other things. 250 gp, mundane.
Combining feycraft and githcraft requires either a team effort by a fey armorer and a gith armorer, or some kind of weird fey-gith hybrid armorer. No rules explicitly detail how to combine these two, but no rule restricts them from being applied to the same armor either. If the combination is unavailable, a single level of Spellsword (Complete Warrior) can handle the remaining Arcane Spell Failure for relatively low cost.
But I would strongly recommend not just allowing the combination, but making it a plot point. A great hero needs an incredible suit of armor, needs to draw upon the skills of not just a master armorer, but multiple master armorers from several completely unrelated races? That sounds like a pretty epic little side-quest. Depends on the campaign, of course.
This has nothing to do with gestures, and everything to do with not losing your focus on the spell. Still Spell has no affect on it.
The Concentration check should be very easy for most mid-level spellcasters. With their low HD and little need for ability scores other than the one used to cast spells, most spellcasters should make Constitution their second-highest ability score, which means starting probably with 14, and picking up a +2 Constitution item sooner rather than later (though after the +2 Int/Wis/Cha item, obviously).
By level 5, you have 8 ranks, should have at least +2 from Constitution, for +10 to begin with. You automatically succeed, then, on 0th- and 1st-level spells, and only need to roll a 2 for 2nd-level spells (95% chance of success) and a 3 for 3rd-level spells (90% chance of success). By 7th level, with 10 ranks, you have a 95% chance of succeeding on 4th-level spells. By 9th, you can automatically succeed in casting any spell you are able to cast.