FAR 61.183 says you need an instrument rating before you can get a CFI certificate so you may have to figure that in as well at your F1 school
True. That's one of the reasons I rushed my IR(A) even when I'm not done with IR(H) yet. Not applicable to heli CFI, plenty CFIs without IR in the rotary part of aviation.
The IR for fixed wing CFI makes sense, since even CPL holders in part 91 flying etc can't fly far without IR.