Answer
It is completely allowed to fast on 15 Shaban and Prophet PBUH has himself does it. According to Hazrat Aaisha Prophet has fasted almost whole month of Shaban and has also asked to fast on 15 of Shaban.
Fasting is allowed by the spirit of Sahi Hadith in Bukhari and Muslim but Sab e Baraat is not proven by Quran and Sahi hadiths also.
All Hadith that are presented in relation with Sab e Baraat are without any doubt ضعیف and موضوع. The number of Hadith that are in Miskhaat (in it’s footnote the number of Hadith and books from which it extracted are also mentioned) are as follows:
1299
1305 to 1308
All are ضعیف Hadith.
But Sheikh Albani said that ضعیف+ضعیف+ضعیف= a hassan Hadith and treated those hadiths as hassan due to presence of many ضعیف hadiths in this regard. But Mohadiseen has never make such principle before.It is solely his own opinion.
Now, from Quran one reference is given regarding Sab e Baraat which is Surah Dukhan (44 number Surah) from Ayah 1 to 6.It mention that Quran is revealed in the Night of Blessing and we all know that it is Sab e Qadr but they said this ayats refers to Sab e Baraat. And other ayahs such as Surah Al Bakarah 185 Ayah make it clear that Quran is revealed in Ramadan which make it clear that in Surah Dukhan Allah is saying regarding Sab e Qadr and Surah e Qadr left no amguity regarding Quran and night in which it revealed.
Hope you would understand it , feel free to ask any question and you have full right to differ from opinion.
Let me inform regarding any weakness in my rational.