The bardic performance countersong gets a lot of flack because most folks think it's useful exclusively versus harpies and sirens the like when, in fact,
Countersong Is Actually Pretty Versatile
I've quoted it below so as to make referencing easier.
[A] bard learns to counter magic effects that depend on sound (but not spells that have verbal components.) Each round of the countersong he makes a Perform (keyboard, percussion, wind, string, or sing) skill check.
So the bard takes a standard action to make a Perform (keyboard, percussion, wind, string, or sing) skill check to start the countersong. Then...
Any creature within 30 feet of the bard (including the bard himself) that is affected by a sonic or language-dependent magical attack may use the bard's Perform check result in place of its saving throw if, after the saving throw is rolled, the Perform check result proves to be higher.
Okay, so that's dumb. Whatever. That's never going to happen. The bard is not going to set up a "countersong shield" in case something sonic or language-dependent happens. He can, of course, but those situations are incredibly rare.
If a creature within range of the countersong is already under the effect of a non-instantaneous sonic or language-dependent magical attack, it gains another saving throw against the effect each round it hears the countersong, but it must use the bard's Perform skill check result for the save. Countersong does not work on effects that don't allow saves. Countersong relies on audible components.
This, however, is incredibly useful. Sonic and language-dependent effects are all over the game, and many of the latter are ongoing and send creatures against their compatriots. Being able to give the fighter another saving throw against the spell suggestion, for example, can be life-saver.
"But How Does the Bard Use It?"
The DM may just tell the characters something like, "When the monster says, 'Defend me from harm,' Regdar turns upon the party," and that's a pretty strong indicator that the effect's language-dependent, but if the DM doesn't make it clear the effect's sonic or language-dependent, the bard may have to identify the effect using conventional means (e.g. Knowledge skill checks, Spellcraft skill checks, previous in-character experience with the monster). The bard (and his party!) will really, really want to identify sonic and language-dependent effects without taking actions--if identification takes a standard action and the bard needs to countersong, he can't until his next turn, and that's too long to wait. The bard should try to become an expert on creatures and effects are vulnerable to his countersong performance so he can start the performance right away.
Once the effect is known to be vulnerable to the countersong performance, the bard takes a standard action to start the countersong. On the affected creature's turn, it gets another saving throw, using the bard's Perform skill check result as the saving throw's result. If the result's high enough the creature's saving throw is successful, and it's as if he succeeded on the saving throw initially.
The special ability soothing voice is a neat but limited trick
The 1st-level half-elf bard racial substitution level replaces countersong with soothing voice (Races of Destiny 157), which is like the bardic song fascinate but different, so below I've inserted soothing voice's differences into the description of the typical bard's fascinate special ability:
A half-elf bard with 3 or more ranks in the Diplomacy skill can use his voice to cause one creature to be affected by a calm emotions effect. The creature to be affected must be within 30 feet, able to hear the bard, must be able to understand the language the bard is speaking, and able to pay attention to him. The bard must also be able to see the creature. The distraction of a nearby combat or other dangers prevents the ability from working. For every three levels a bard attains beyond 1st, he can target one additional creature with a single use of this ability.
To use the ability, a bard makes a Diplomacy check. His check result is the DC for the affected creature’s Will save against the effect. If a creature’s saving throw succeeds, the bard cannot attempt to fascinate that creature again for 24 hours. If its saving throw fails, the creature is affected as if by the spell calm emotions [Note: Several omitted sentences appear here that the DM could, potentially, apply also to the special ability soothing voice, but I have assumed here they are, instead, relevant to the special ability fascinate. Ask the DM.]
This effect is an enchantment (compulsion), mind-affecting ability.
While the spell calm emotions is usually is a 2nd-level spell (therefore usually not available until at least character level 3 and higher than that for a bard), its usual range is medium, its usual area is a 20-ft.-radius spread, and its usual duration is concentration (up to 1 round/level). Although the special ability soothing voice's save DC will be higher than the spell—based as it is on a Diplomacy skill check—, a low-level character being able to use a few times per day this special ability (that draws its uses from the same pool as inspire courage, by the way) isn't overpowered, especially considering that the bard must have languages sufficient to be able to make himself understood to the creature (unlike the song fascinate) and that affected creature can just walk away if the bard's uninteresting (which is insulting and hilarious).
At higher levels, soothing voice is probably a waste of the bard's time, with him having much better things to do with his bardic music ability and him having spells that will do what he was trying to do with soothing voice better than soothing voice, but soothing voice may yet even then give the bard the opportunity to use his real Diplomacy skill, a skill that can wreck the game in the wrong hands. That is, at least, until higher levels in which the vast majority of creatures are immune to mind-affecting effects (you know, like the special ability soothing voice).
Note that spell calm emotions neither erases memories nor changes attitudes. If Baracs strolls into the orc camp, murders the orc warlord, is caught red-handed by the warlord's lover, uses soothing voice on the warlord's lover, and the lover fails the saving throw, the lover will (greatsword in hand) calmly discuss with Baracs his actions and impending demise as he escorts Baracs to a cell. The warlord's lover, even while affected by the spell calm emotions, can still call for help, alerting the camp, and Baracs just won't have enough soothing voices for the whole tribe. And the minute Baracs tries something aggressive (and a DM may rule that a murderer caught red-handed who then tries to flee a crime scene is behaving aggressively), all bets are off, and swords start swinging.
The spell calm emotions gives the caster a brief respite in which to catch his breath and perform some minor, non-aggressive actions, most often the spell offering an opportunity to for the party to enter into an otherwise implausible parley. It does shut down melee attackers, but while the effect lasts it also essentially shuts down the party. (That is, "The distraction of a nearby combat or other dangers prevents the ability from working.") Unless the party's worked out tactics beforehand for ambushing becalmed monsters (which is at least rude if not outright evil), the only thing a calm emotions effect will really do is let the user talk to one or more creatures that were, moments before, trying to kill him.
I can imagine that might be overpowered in some campaigns, but I suspect those campaigns probably wouldn't allow such a special ability to be taken in the first place.
Best Answer
RAW, yes Inspire Courage is not given a range and therefore would be able to affect all friendly targets that could perceive the Performance.
Perception DC 5 (battle is Terrible Conditions) +1/10ft to hear/see the performance.
The rules don't account for a Bard to be able to project the bonuses through magic, but it follows that increasing their volume could extend the range. Anything else would have to be discussed with the GM. If you're going to argue that seeing an image of an inspirational dance can inspire you, consider if you've ever watched a concert video and not been excited like you would be at a live show.
Postscript, it is not unusual to homerule Inspire courage to have a 30ft range based on nearly every other Bardic Performance, including ones with similar affects.