Question 1: Is the above even a correct RaW? or have I missed something?
Well, there's a funny thing about firesnake's RAW. From an extremely technical standpoint, your reading of firesnake is incorrect. This is because Tome of Battle recieved an errata back in 2008. Firesnake's text was changed, clearing up the RAI on what it's apparently meant to do:
Page 53 – Firesnake
Remove last two sentences of first paragraph. Substitute last two sentences of second paragraph with “A c Page 37 – Alacritous Cogitation [Addition] Revise end of first sentence to read, “...cast any arcane spell you know of the same level or lower and of casting time no longer than 1 round.” Page 47 – Storm Bolt [Addition] Under benefits, add “A successful Reflex save halves damage.” Page 50 – Becoming an Abjurant Champion [Substitution] The section on becoming an Abjurant Champion should read, “...any martial-oriented character can qualify by taking minimal levels in an arcane spellcasting class, such as one level in wu jen or two levels in bard.” Page 51 – Abjurant Champion Class Features [Deletion] Under the abjurant armor ability, remove mention of “mage armor” at the end of the paragraph. The abjurant armor ability does not affect mage armor, but the spell is still useful to an abjurant champion. Page 70 – Expanded Spellbook [Revision] First sentence should read, “When you reach 2nd level, you can add one wizard spell of your chosen school to your spellbook.” Page 71 – Moderate School of Esoterica [Addition] Add the following to the last sentence of the first paragraph of this ability’s decription, “(Unless otherwise noted)”. Page 96 – Arcane Fusion [Addition] Include clause, “If applying a metamagic feat to a spell, use the adjusted spell level and casting time for purposes of determining eligibility for Arcane Fusion.” Page 98 - Caustic Mire [Addition] Spell type should read “Conjuration [Acid]” Page 98 - Caustic Smoke [Addition] Spell type should read “Conjuration [Acid]” Page 99 - Channeled Sound Burst [Revision]/[Addition] Area should indicate to “See text” The option for expending 2 full rounds to cast the spell should indicate that the spell’s caster is unaffected by the spell’s effects. Page 101 - Deadly Sunstroke [Substitution] Spell type should read “Evocation [Fire],” not “Evocation [Light]” Page 06 – Heart of Air [Substitution] The spell’s “wu jen 2 (air)” tag should instead read “wu jen 2 (general).” Page 108 - Immediate Assistance [Substitution] Should be of the Transmutation school. Page 110 - Melf's Slumber Arrows [Substitution] Spell’s short entry should read “Will partial” instead of “Fortitude partial.” Page 114 - Reaving Aura [Revision] The last sentence should read, “This spell has no effect on creatures that have more than 0 hp.” Page 119 - Tactical Teleport [Deletion] This spell targets only willing creatures, so the sentence that reads, “Only objects held or in use (attended) by another individual receive savings throws and spell resistance,” should be removed. Similarly, the Saving Throw entry at the top should not include a Will save for objects because they cannot be targeted. Page 123 – Cold Comfort [Substitution] “Least” should replace “Lesser.”
Naturally, this is not very useful for our purposes at all. So instead of using the completely true and 100% official RAW, I'm going to step through the maneuver itself:
Initiation Action: 1 standard action
Range: 60 ft.
Saving Throw: Reflex half
So, as a standard action, you initiate the firesnake maneuver and create a Special area within 60 feet. This is an intantaneous effect, and as such, you don't have to concentrate or otherwise direct it later. Reflex half, so anything that takes damage from it gets a save to reduce the damage. Now, let's see what it actually does:
When you initiate this maneuver, you cause a line of fire to twist across an area to burn your enemies. This line is 60 feet long. Unlike a standard line, a firesnake can bend and twist to hit your foes. A firesnake starts in an adjacent square.
So the first part of our Special area is this thing. It's a line that can be twisted as you like when you make it, and otherwise would function as a line. It doesn't quite define how twisty you can make it, but it'll do for our purposes. Next up, the fun bits:
It can move up to 60 feet each round. It can move out of your line of sight or line of effect, but you gain no special knowledge of the areas it moves into. If a firesnake moves into a creature’s space, that creature takes 6d6 points of fire damage, with a Reflex save (DC 14 + your Wis modifier) for half damage. A creature can only take damage from the firesnake once in a single round. It makes the saving throw and takes damage the first time that the firesnake touches it. After that, a firesnake has no effect on that creature. A firesnake must move along the ground. It cannot fly, and it pays the standard movement penalties for difficult terrain and other effects.
This maneuver is a supernatural ability.
Note that since this is an instantaneous ability, and it doesn't have any provisions for you controlling it, you don't actually get to. Once you create the firesnake, it can move up to 60 feet each round, and it can move out of your line of sight or line of effect. It can only damage a person once, after which it stops being able to harm them, and it cannot damage objects, because it only deals damage when it moves into a creature's space. You can have as many made as you feel like, but you still won't be able to direct them at all without DM adjudication (although how they would move, not being creatures themselves, is up in the air. Maybe they're like curious puppies).
I would definitely caution you against wantonly creating firesnakes, on account of their mindlessness, uncontrollableness, and general immortality. Given the current time of year, maybe a public service announcement is in order.
Question 2: Is the spell intended to last forever, 1 round, or some other duration?
Question 3: Assuming duration is long enough to allow this to happen, is the intention that I can create multiple of these simultaneously?
Sadly, we have no way of knowing what the duration of the maneuver was meant to be, and if multiples are meant to be allowed. They had their chance to fix it with the errata and managed not to do so, in the most spectacular way possible. The RAW is that it's instantaneous and you can have as many as you make, and that's all there is to go on. There are no references to the maneuver on the wizards website, and it doesn't even show up in the 3.5 FAQ.
Question 4: Am I reading the linked homebrew errata correctly?
The only real differences between the original firesnake maneuver and the homebrew fix is that the firesnake moves up to 60 feet as part of initiating the maneuver, that it can move over any horizontal surface, not just the ground, and that it is not explicitly noted as being able to move out of line of sight or line of effect. However, instantaneous effects don't care about range once they're actually used, so it doesn't do anything to solve the unlimited use and duration problem, nor the problem of the maneuver not actually allowing you to direct it (which is normally done in similar spells by listing an action to do so). I don't think this is a very good fix to use, myself.
Question 5: Does anyone have any links to official errata/posts on the subject(I couldn't find any), or any homebrew that they have used and found to be balanced, or that has attained widespread usage
There is no official errata or post that makes firesnake into something usable. Even more sadly, there's very little homebrew or fixes for the maneuver floating around on the internet. The one you linked is the only one I could find that actually attempted to fix it, even if they failed at it.
Question 6: Failing anything, can I get a review of the following homebrew rules.
These houserules for firesnake are fair. There are some minor wording quibbles; I'd change the duration of the maneuver to "Permanent (D)", and note that it's a free action to direct the firesnake's movement during your turn. One thing to note is that while this solves the problem of firesnake being completely nonfunctional, it doesn't actually make it a good maneuver. Were I rewriting it, I would probably make it deal 1d6 damage per initiator level to a given target, because it has a relatively low save DC for scaling into later levels, and a cool, flavorful maneuver dealing 6d6 damage at level 20 is pretty underwhelming.