Is there a way to use TouchID for iTunes and App store only?

After each time you reboot the phone, it will demand the unlock code. Only once that has been successfully entered will it then allow TouchID.

Same applies to initial login & also iTunes.

Having TouchID enabled makes it always lock when switched off, there is no grace period for switching it back on within the 'lock after…' period, like devices without TouchID.

Sorry for my image being Dutch, but you can disable the unlock functionality easily after setting it up correctly.

No, you need to have a password in case Touch ID doesn't work. There's no way (at least without jailbreak) to get this 'fixed'.