PFSRD > Magic > Duration > Concentration

Concentration

The spell lasts as long as you concentrate on it. Concentrating to maintain a spell is a standard action that does not provoke attacks of opportunity. Anything that could break your concentration when casting a spell can also break your concentration while you're maintaining one, causing the spell to end. See concentration.

You can’t cast a spell while concentrating on another one. Some spells last for a short time after you cease concentrating.

Thus,

• What action am I allowed while I am concentrating? Can I move? Attack? Cast another spell?

It takes your standard action. You can use your other actions as you please, to move or attack (e.g. an attack of opportunity), so long as they don’t require a standard action. The only special exception is spellcasting; you can’t do that even if it’s a swift-action spell.

• Can I decide to stop concentrating at any time?

Somewhat vaguely defined. Certainly, on your turn you can choose not to spend your standard action to concentrate and thus the spell immediately ends. And someone else can forcibly end your concentration outside your turn, by forcing a Concentration check that you fail. Thus, I feel that it would be unreasonable to deny you the ability to end concentration at any time you like.

• Do the effects end immediately on me ending my concentration (either through interruptions or voluntarily)?

Depends on the spell. Precipitate, yes. Other spells have durations like “Concentration + one round,” and those would linger for the indicated amount of time.

A barbarian/bard can, while in a rage, start and continue a bardic performance—maybe

The bard's bardic performances say nothing about concentrating and only a handful mandate Perform skill checks (countersong, distraction, et al.), making the others possibly usable while in a rage. However, performances do require using some kind of action to start and, often, to maintain. So while it's totally legit to get really angry and, for example, climb a mountain or swim a channel, because bardic performances use actions, starting or maintaining them while in a rage might run afoul of this part of the rage description:

While in rage, a barbarian cannot use any Charisma-, Dexterity-, or Intelligence-based skills (except Acrobatics, Fly, Intimidate, and Ride) or any ability that requires patience or concentration.

Emphasis mine. So while the barbarian's rage itself doesn't explicitly forbid, for example, massive shredding on your lute or belting out "99 Bottles of Dwarven Ale on the Wall" while simultaneously furiously headbutting orcs to death, the GM can simply say No, starting and maintaining a bardic performance requires patience that's impossible while raging.

This GM would allow a character in a rage to start or continue an appropriate bardic performance

The player should be aware that it's a tough row to hoe, though. In addition to other issues like multiple ability score dependency,¹ the huge—perhaps, I dare say, insurmountable—problem with playing, for example, a barbarian 3/bard 4 is that such a character will each day have only a total of 11 rounds of fight in him (and that's generously assuming a Con 16 and Cha 16).² Level 7 is actually past the point when the wizard can cast an extended rope trick and everybody can rest in the extradimensional space in relative safety, so being good for only two fights per day (unless the group's really efficient) is fine at that point, but actually playing this character to that point would be a constant and—for me, anyway,—unpleasant war with an ever-ticking clock.

¹ Such a character needs high Str, Con, and Cha, would like a high Dex and Int, and will regret a low Wis.
² Yes, I'd put the extra level in bard. That means 2nd-level bard spells.