It won't fix *everything*.
If you're having cold start issues already then it would be worth looking over the car, Japan has snow.. Much colder than here, the car is built from factory to be able to start in the cold.
"High RPM issue", I'll take a stab and guess you're having misfire in high RPM? Also not likely to be fixed by a tune, coilpacks are a common cause for this, also check plugs.
R&R, yes it will help with this, however an r32 actuator should be getting you 10psi if hooked up without a boost controller, as far as I'm aware most 33's can take 10psi (including mine) without R&R unless there is an issue with the AFM.
A tune will help with economy and power, especially with the change in boost levels, it can also help diagnose what other sensors etc might be faulty and causing troubles.
Take it up with willall since thats who you want to do the work, they'll be able to give you the best answers