Does what I did, by arousing desire before sleep with the intention of having a wet dream to ejaculate, count as masturbation that necessitates making up the day (qada'), expiation (kaffara), and fulfilling the vow (nazr)? And can this day be made up with the intention of both fasting and fulfilling the vow simultaneously?

The semen that was discharged from you during sleep is due to a wet dream, and it does not invalidate the fast, whether you anticipated a wet dream or not. The reading of fatwas should be with the intention of learning and benefiting, not for arousing lust, lest it lead to masturbation. Your fast is valid, and you are not required to make up the day or offer expiation. What you did is not masturbation. Your third question is unclear.