Why the Rachni wars?

Sovereign didn't want to be discovered because it would likely lead to what happened at the Battle of the Citadel, so he used the rachni the same way he used the geth.

Why not? It's nice to test the enemy out, and carry a mission out with as few casualties as possible. The Reapers seem to be attracted to the hive minds for manipulation, so rachni is an organic version of geth. I dunno, I never really thought it was odd.

The reapers were unable to indoctrinate rachni queens.  It's implied that the leviathans may have caused that war.

To weaken the races.  If the rachni make them weak they're much less prepared to face the Reapers when they come.  

But if they wanted to weaken the races, why wait so long between the war and the invasion?

Well, I do remember Javik saying that his people breed the rachni to the point they rebelled. The Reapers were probably aware of their presence but the rachni might not have achieved space flight prior at that point. They had about 50,000 years to get that going.

When the queen talks about the machines and the "sour yellow note," I always thought it was Sovereign that started the war. Throwing the spacefaring races into chaos before the arrival of the Reaper fleet would have come in handy. Sovereign might have started the war to use the Rachni to take control of the Citadel, or at least distract the galaxy while he started quietly indoctrinating people.

That didn't work so well, since Sovy couldn't have seen the uplift of the Krogan happening. It's just my theory anyway.

except that it revealed a two sided conflict that had been going on for millenia.

Leviathan in a way lost - hence why they're in hiding.  Why they feel the need to use globes to observe the universe from their hiding places.

The tone (note the Rachni queen does use a singular form here) from space that caused the Rachni to sing with it's own sour yellow note can only be Sovereign and Sovereign alone -  since the Rachni Wars occurred within the current cycle.  You haven't yet reached the point in ME1 where Vigil explains that Sovereign is essentially a solitary Reaper cut off from being able to call in the other Reapers because the keepers are not responding to it's commands to initiate the harvest.  Vigil also indicates that Sovereign may have tried to enlist several species as allies to help try to take the Citadel (just like it ultimately used the geth).  Vigil clearly says that Sovereign would not have been able to just take the Citadel alone because it was a lone Reaper cut off from the others and would, if it attacked, be facing all the species by itself and "even a Reaper could not survive such odds."  (Of course, the player has to undertake to "investigate" things with Vigil in order to hear all of this description.)  How Sovereign went about causing the Rachni to "sing with it's own sour yellow note" is not described in the game.

The Rachni (along with several other of the current species) were in the process of being uplifted by Protheans.  Javik (if you have the DLC) talks about this several times during ME3.  He indicates also that they abandoned the uplifts because they hoped the Reapers would leave these "primitive" species alone to carry one into the next cycle.  It is clear that part of the Prothean strategy was to find ways to pass knowledge along into the next cycle... in case the Protheans themselves did not survive.  Ensuring that as many species as possible (at various different stages of uplift) are left alone by the Reapers is one way to make it likely that things like the plans for the Crucible do get found and perhaps used by the subsequent cycle to eventually defeat the Reapers. 

However, Javik does indicate that the Rachni uplift was primarily to use them as weapons and it did result in the Protheans engaging in a war against the Rachni in which the Rachni were thought by the Protheans to have been exterminated.  Apparently, the rachni went into hiding at that point and, therefore, avoided actual extermination.  Their hiding was disturbed sometime before 186 CE (per ME3 codex - "Over 2,000 years ago, explorers foolishly opened a mass relay to a previously unknown system and encountere something never seen before or since: a species of spacefaring insects guided by a hive-mind intelligence.  Unfortunately, the rachni were not peaceful, and the galaxy was plunged into a series of conflicts known as the Rachni Wars.  Attempts to negotiated were futile, as it was impossible to make contact with the hive queens that guided the race from beneath the surface of their toxic homeworld." - note the use of the plural here) 

If the Rachni Queen is killed on Noveria, the Breeder Queen that appears in ME3 describes herself as a "monster."  If she is released, she proves herself to be "untrustworthy" (word used in the Wiki) and the player's War Assets are affected in a negative way.  Although she says things in order to cause Shepared to release her, she either has been indoctrinated or has been engineered in other ways to be loyal to the Reapers.  The Rachni Queen from Noveria is resistant to being indoctrinated... but I'm not convinced that is actually an indication that all Rachni queens are immune to indoctrination.  If the queens themselves were all immune to indoctrination, it must then be that the hidden queens were not in control of the rachni soldiers (who had been "forced to sing with its own sour yellow note" by Sovereign)

One irony about the Rachni being used by Sovereign to try to take the Citadel in 1 CE (per Wiki)... means that the harvest for that current cycle was meant to begin BEFORE humans had achieved space flight.  Had the Krogan not been uplifted and defeated the Rachni, humans would have likely been left alone to survive into the subsequent cycle.  They just never would have met the Asari, Turians, or Salarians since those species would have been the ones to have been harvested.

Although, somewhat confusingly, this reference contains a plural ("those who soured") and, of course, in ME2, we know that Shepard is no longer seeking to bring down just Sovereign (been there, already did that)... but rather he/she is seeking out a way to stop the rest of the Reapers. 

However, given the time frame given for the Rachni Wars (i.e. long after the Prothean extinction and after the reapers, except Sovereign, had retreated to dark space), I tend to consider/dismiss that plural a bit of an "error" in the lore.  However, it is possible that it may be an indication that more than one Vanguard Reaper was left behind inside the galaxy.  However, that then begs the question as to why Sovereign did not just assemble those other vanguard reapers together and attack the Citadel directly without trying to elicit any other species as allies (i.e. the rachni or, later, Saren and the geth).

(Pure speculation... Might it mean that the Krogan or that the Rachni queens had successfully killed off the other vanguard Reapers except for Sovereign and that history was just never revealed to us?)

The question is when did the Reapers try to manipulate the Rachnni. The queen was found on a ship floating in space since the end of the Rachni War.

How long is the gestation period of a queen?

... or perhaps the cold in space effectively froze and preserved the egg that was hatched to become the Rachni Queen we meet on Noveria?  The gestation of the eggs doesn't seem to be that long - a single queen can produce "a colony within weeks" (per ME1 dialogue... forget right now though who actually said it - Tartokovsky??)... and we do freeze sperm and eggs all the time for use later IRL.

The Noveria Queen's dialogue indicates that, as an egg, she was listening to the Rachni Wars take place.  A "tone from space" forcing the rachni to "sing with it's own yellow note" meaning Sovereign indoctrinating them... and then hearing her "mother cry in her dreams" as her mother is killed during the Rachni Wars, and then the sky falling silent as the Rachni become extinct.  It seems obvious to me that her egg was laid by her mother while she was on a ship fighting during the Rachni Wars... and because the ship became "derelict" after she and the others aboard it were killed, the environment became cold enough that the egg was frozen before it hatched and remained drifting in space until discovered by the Binary Helix scientists... who brought it to Noveria, warmed it up, and hatched it.

The one thing that does not make sense to me about the Rachni Queen is that she is, somehow, portrayed as being both peaceful and sane despite not having grown up with her mother singing to her... unless the mother's singing really only matters during the early stages of the egg development.

(More pure speculation - I know this might be opening up a can of worms, but the thought just crossed my mind that perhaps being frozen is one thing that makes an organic brain resistant to indoctrination... the Noveria Queen is resistant and her age was frozen and Shepard was frozen as well... of course, such a thing would discount the indoctrination theory...)