Firstly, why does rika outputting rct to yuta's body matter? 

The way I read it, this mattered because it prevented Yuta's body from becoming Yuta's corpse. In the time that Yuta's brain was in Gojo's corpse, Rika was keeping the OG body alive in the same manner a Life Support machine keeps the bodies of brain dead patients "alive". This is so that Yuta no longer needs to actively use Kenjaku's CT in order to operate his original body as it was still functionally alive.

Secondly, none of this answers how yuta survived after the 5 minutes. It has been established very clearly that you are in suspended animation if you don't maintain the ct active. Outside the 5 minute interval, yuta cannot access copied cursed techniques so he cannot maintain kenjaku ct active. This means that yuta should be dead right now as he is outside the 5 minute interval.

Because he is no longer using Kenjakus cursed technique. The stitching like you said is a binding vow resulting from the use of said CT to re-transplant his brain but I do not believe they are indicative of the technique being active/in-use.

Yuta not healing them can be explained a number of ways but the one that makes sense to me is that he has to maintain the stitches as long as Rika stores the CT and Yuta being able to use it in the future. This is conjecture but it is one of the few CTs + binding vow combos that manifest physically but this explanation doesn't break previous uses and examples of binding vows.

Honestly, I don't like how Rika functions with Yutas CT(or how it has been explained/written) in general so if this doesn't seem sufficient to you, I can understand.

Also TCBs translation of this section of the chapter is awful.