Tzeentch Daemons question

[Charsiupao]

When using Split (or Split Again), the rules say "Set up 2 (1 for Split Again) new fighter(s)...". Does this mean that the new Blue Horrors or Brimstone Horrors are treated as new, and have yet to activate? If I had a wounded Pink Horror, could I move him twice, activate Split, and have two Blue Horrors (within 3" of the old Pink's position) ready to continue moving forward during my next activation?

Are Split Units considered part of the original unit for "protect unit" missions? If the objective was to, say, protect your Dagger (and take down the opposing Dagger), could I really frustrate my opponent by Split (and Split again), making it a nightmare for them to kill off my entire Dagger who are scattering all over the place, or do I lose the game the moment I Split my last Pink Horror in my Dagger? The rules say that "this fighter is taken down", so I do lose the Pink Horror, but are the new units automatically counted as part of the group which they spawned from (in which case the Dagger lives on)?

Thanks for any advice! I'm new here and registered this account just to ask this, but I'm sure I'll have many more questions over the coming months!

[Charsiupao]

I found the answer to the second question in this errata:-

https://www.warhammer-community.com/wp-content/uploads/2019/10/3bd97281.pdf

DISCIPLES OF TZEENTCH: DAEMONS

Q: The abilities ‘Split’, and ‘Split Again’ add new fighters to your warband. How does this interact with victory cards such as ‘No Mercy’ and ‘Dominate’?A: The new fighters are added to your warband but are not part of any battle group. This means that in ‘No Mercy’, these new fighters are counted when determining the victory condition, whereas in a battle using ‘Dominate’ or a similar victory card, they are not.

[Kramig]

By now I considered that blue horrors (and brimstone) can be activated and perform their 2 actions