[RPG] Does Haunting Melody use a Standard Action

Within 3.5e D&D you cannot use an inaudible performance for Bardic Music. Bardic Music specifically states (from the d20 SRD):

While these abilities fall under the category of bardic music and the descriptions discuss singing or playing instruments, they can all be activated by reciting poetry, chanting, singing lyrical songs, singing melodies, whistling, playing an instrument, or playing an instrument in combination with some spoken performance.

Note that only audible forms of performance are listed.

While there is no particular rules-based reasoning for this, I would assume the logic-based reason is something along the lines of: you can't counter a sonic or language-based effect with a mime (Countersong), and it would be otherwise quite difficult for your allies to focus on you enough in a combat situation to gain a benefit from a purely physical performance (Inspire Courage/Competence/Greatness/Heroics).

If your GM is willing, you could instead use all or some of the rules from Pathfinder's Bardic Performance which covers uses of purely physical Perform skills.

Yes, by RAW you can.

As per SRD, while starting bardic music is always a standard action, maintaining it is another story. Bardic music abilities requiring concentration to maintain explicitly say so, for example (emphasis mine),

Inspire Competence (Su)

A bard of 3rd level or higher with 6 or more ranks in a Perform skill can use his music or poetics to help an ally succeed at a task. The ally must be within 30 feet and able to see and hear the bard. The bard must also be able to see the ally.

The ally gets a +2 competence bonus on skill checks with a particular skill as long as he or she continues to hear the bard’s music. Certain uses of this ability are infeasible. The effect lasts as long as the bard concentrates, up to a maximum of 2 minutes. A bard can’t inspire competence in himself. Inspire competence is a mind-affecting ability.

Therefore, whether you can do something meaningful while maintaining Inspire Courage is up to the interpretation of the duration clause (why don't you just resort to these 5 rounds, or 1 minute?).

The effect lasts for as long as the ally hears the bard sing and for 5 rounds thereafter.

The description of the perform skill does not shed any light at this problem either (emphasis mine):

Action Varies. Trying to earn money by playing in public requires anywhere from an evening’s work to a full day’s performance. The bard’s special Perform-based abilities are described in that class’s description.

To sum up,

there is no action stated in the rules to maintain the Inspire Courage, so we can assume it is a free action. Therefore you're free to do whatever you want while singing (reciting, in your case), as long as you have requisite numbers of hands free (you probably do) and it is not prohibited by bardic music rules explicitly (cast spells, activate magic items by spell completion (such as scrolls), spell trigger (such as wands), or command word).

As a note,

the concentration on the bardic music is akin to the concentration on a spell; it even prohibits other casting. You could ask your DM if Extraordinary Concentration could be applied to the bardic music, too. Swift Concentration could also be useful for you, since it is already applicable.