Ok here is my definitive feedback and arguments for @Eljay’s questions.
1) Barbed Broadsword - it should definitelly be included. There is exactly zero evidence against prime Tuyet weilding it, and all the evidence for it. Greg specifically said he would reveal Tuyet’s tool in the upcomming serial (and he did).
Also, the alternate versions of characters always have the same masks and tools as their prime universe counterparts, unless there is a very specific reason for otherwise (such as the Melding AU, etc.). Not only are the tools shared between universes by default, but there are in fact other toa tools which have only explicitly appeared in alternate universes, such as recently canonized Seismic spear and Sub-zero spear. The point about the Barbed Broadsword only appearing in AU is therefore utterly non-applicable as a counter argument.
Since we want our characters to be fully equiped with their standard gear, its inclussion should be mandated at least at some stage of the contest.
2) Nui Stone - this object’s inclusion is also necessary at some point during the contest. Here are the reasons.
Nui Stone is in fact a standard equipment for Tuyet and it is no exaggeration to say it is her primary signature weapon. She has had it pretty much her entire life as a Toa - for an undisclosed period of time on her home island and then ever since she moved to Metru Nui the Nui Stone was still in her possession (and in use).
Even after her exile, she has been using it for tousands of years to drain other Toa of their Toa Power and by her own admission considered it her personal superweapon. In other universes as a direct consequence of her usage identical to that in prime reality, she became widely known as “The wielder of the Nui Stone”. It is an integral part of not only her arsenal, but her entire character - at one point it was LITERALLY a part of her being.
It is for these reasons Tuyet should have her Nui Stone with her in the intact form (since she spent the most time with that form). It is even more important than the Barbed Broadsword. Even if only in the artwork, but it has to be there. There is no Tuyet without Nui Stone.
3)Re-using Helryx entries for Tuyet - yes of course. This was already allowed during the Helryx contest and as other have pointed out is even in the rules.
4) The build - there is none reason to mandate any kind of build and should be left for creativity of entrants. If anything, entrants should be encouraged (though again not mandated) to make Tuyet visually distict from Lhikan.
Toa Mangai are not originally fro the same team. They came together from all corners of the universe to finght of a threat and only stuck together afetr the fact. Even more relevant to this particular contest, we know Tuyet explicitly came from adifferent homeland than Lhikan, so there is no reason for any parity between the at all.
And there it is.